diff --git a/composer.json b/composer.json
index b3956a887564..93d6b029d8c1 100644
--- a/composer.json
+++ b/composer.json
@@ -20,7 +20,6 @@
         "ext-xml": "*",
         "doctrine/event-manager": "~1.0",
         "doctrine/persistence": "~1.0",
-        "fig/link-util": "^1.0",
         "twig/twig": "^1.41|^2.10",
         "psr/cache": "~1.0",
         "psr/container": "^1.0",
diff --git a/src/Symfony/Bridge/Twig/Extension/WebLinkExtension.php b/src/Symfony/Bridge/Twig/Extension/WebLinkExtension.php
index 0ca519ee7242..63bfa2eba026 100644
--- a/src/Symfony/Bridge/Twig/Extension/WebLinkExtension.php
+++ b/src/Symfony/Bridge/Twig/Extension/WebLinkExtension.php
@@ -11,9 +11,9 @@
 
 namespace Symfony\Bridge\Twig\Extension;
 
-use Fig\Link\GenericLinkProvider;
-use Fig\Link\Link;
 use Symfony\Component\HttpFoundation\RequestStack;
+use Symfony\Component\WebLink\GenericLinkProvider;
+use Symfony\Component\WebLink\Link;
 use Twig\Extension\AbstractExtension;
 use Twig\TwigFunction;
 
diff --git a/src/Symfony/Bridge/Twig/Tests/Extension/WebLinkExtensionTest.php b/src/Symfony/Bridge/Twig/Tests/Extension/WebLinkExtensionTest.php
index 332165571c9a..1739c1ee9183 100644
--- a/src/Symfony/Bridge/Twig/Tests/Extension/WebLinkExtensionTest.php
+++ b/src/Symfony/Bridge/Twig/Tests/Extension/WebLinkExtensionTest.php
@@ -11,11 +11,11 @@
 
 namespace Symfony\Bridge\Twig\Tests\Extension;
 
-use Fig\Link\Link;
 use PHPUnit\Framework\TestCase;
 use Symfony\Bridge\Twig\Extension\WebLinkExtension;
 use Symfony\Component\HttpFoundation\Request;
 use Symfony\Component\HttpFoundation\RequestStack;
+use Symfony\Component\WebLink\Link;
 
 /**
  * @author Kévin Dunglas <dunglas@gmail.com>
diff --git a/src/Symfony/Bridge/Twig/composer.json b/src/Symfony/Bridge/Twig/composer.json
index a21b3c288cf8..bddfe8bee55b 100644
--- a/src/Symfony/Bridge/Twig/composer.json
+++ b/src/Symfony/Bridge/Twig/composer.json
@@ -42,7 +42,7 @@
         "symfony/console": "^3.4|^4.0|^5.0",
         "symfony/var-dumper": "^3.4|^4.0|^5.0",
         "symfony/expression-language": "^3.4|^4.0|^5.0",
-        "symfony/web-link": "^3.4|^4.0|^5.0",
+        "symfony/web-link": "^4.4|^5.0",
         "symfony/workflow": "^4.3|^5.0"
     },
     "conflict": {
diff --git a/src/Symfony/Bundle/FrameworkBundle/Controller/ControllerTrait.php b/src/Symfony/Bundle/FrameworkBundle/Controller/ControllerTrait.php
index 9cb7a58f6e85..14e62f074b24 100644
--- a/src/Symfony/Bundle/FrameworkBundle/Controller/ControllerTrait.php
+++ b/src/Symfony/Bundle/FrameworkBundle/Controller/ControllerTrait.php
@@ -12,9 +12,8 @@
 namespace Symfony\Bundle\FrameworkBundle\Controller;
 
 use Doctrine\Common\Persistence\ManagerRegistry;
-use Fig\Link\GenericLinkProvider;
-use Fig\Link\Link;
 use Psr\Container\ContainerInterface;
+use Psr\Link\LinkInterface;
 use Symfony\Component\Form\Extension\Core\Type\FormType;
 use Symfony\Component\Form\FormBuilderInterface;
 use Symfony\Component\Form\FormInterface;
@@ -33,6 +32,7 @@
 use Symfony\Component\Security\Core\Exception\AccessDeniedException;
 use Symfony\Component\Security\Csrf\CsrfToken;
 use Symfony\Component\WebLink\EventListener\AddLinkHeaderListener;
+use Symfony\Component\WebLink\GenericLinkProvider;
 
 /**
  * Common features needed in controllers.
@@ -420,7 +420,7 @@ protected function dispatchMessage($message, array $stamps = []): Envelope
      *
      * @final
      */
-    protected function addLink(Request $request, Link $link)
+    protected function addLink(Request $request, LinkInterface $link)
     {
         if (!class_exists(AddLinkHeaderListener::class)) {
             throw new \LogicException('You can not use the "addLink" method if the WebLink component is not available. Try running "composer require symfony/web-link".');
diff --git a/src/Symfony/Bundle/FrameworkBundle/Tests/Controller/ControllerTraitTest.php b/src/Symfony/Bundle/FrameworkBundle/Tests/Controller/ControllerTraitTest.php
index aa03b2d13fab..fd064bb15b1a 100644
--- a/src/Symfony/Bundle/FrameworkBundle/Tests/Controller/ControllerTraitTest.php
+++ b/src/Symfony/Bundle/FrameworkBundle/Tests/Controller/ControllerTraitTest.php
@@ -11,7 +11,6 @@
 
 namespace Symfony\Bundle\FrameworkBundle\Tests\Controller;
 
-use Fig\Link\Link;
 use Symfony\Bundle\FrameworkBundle\Controller\ControllerTrait;
 use Symfony\Bundle\FrameworkBundle\Tests\TestCase;
 use Symfony\Component\DependencyInjection\Container;
@@ -29,6 +28,7 @@
 use Symfony\Component\Security\Core\Authentication\Token\UsernamePasswordToken;
 use Symfony\Component\Security\Core\User\User;
 use Symfony\Component\Serializer\SerializerInterface;
+use Symfony\Component\WebLink\Link;
 
 abstract class ControllerTraitTest extends TestCase
 {
diff --git a/src/Symfony/Bundle/FrameworkBundle/composer.json b/src/Symfony/Bundle/FrameworkBundle/composer.json
index 5e3a699e3dc1..152f1b65a5a2 100644
--- a/src/Symfony/Bundle/FrameworkBundle/composer.json
+++ b/src/Symfony/Bundle/FrameworkBundle/composer.json
@@ -31,7 +31,6 @@
     },
     "require-dev": {
         "doctrine/cache": "~1.0",
-        "fig/link-util": "^1.0",
         "symfony/asset": "^3.4|^4.0|^5.0",
         "symfony/browser-kit": "^4.3|^5.0",
         "symfony/console": "^4.3|^5.0",
@@ -58,7 +57,7 @@
         "symfony/workflow": "^4.3|^5.0",
         "symfony/yaml": "^3.4|^4.0|^5.0",
         "symfony/property-info": "^3.4|^4.0|^5.0",
-        "symfony/web-link": "^3.4|^4.0|^5.0",
+        "symfony/web-link": "^4.4|^5.0",
         "doctrine/annotations": "~1.0",
         "phpdocumentor/reflection-docblock": "^3.0|^4.0",
         "twig/twig": "~1.34|~2.4"
diff --git a/src/Symfony/Component/WebLink/CHANGELOG.md b/src/Symfony/Component/WebLink/CHANGELOG.md
index 2204282c26ca..28dad5abdd74 100644
--- a/src/Symfony/Component/WebLink/CHANGELOG.md
+++ b/src/Symfony/Component/WebLink/CHANGELOG.md
@@ -1,6 +1,11 @@
 CHANGELOG
 =========
 
+4.4.0
+-----
+
+ * implement PSR-13 directly
+
 3.3.0
 -----
 
diff --git a/src/Symfony/Component/WebLink/GenericLinkProvider.php b/src/Symfony/Component/WebLink/GenericLinkProvider.php
new file mode 100644
index 000000000000..5c8b2e71144d
--- /dev/null
+++ b/src/Symfony/Component/WebLink/GenericLinkProvider.php
@@ -0,0 +1,83 @@
+<?php
+
+/*
+ * This file is part of the Symfony package.
+ *
+ * (c) Fabien Potencier <fabien@symfony.com>
+ *
+ * For the full copyright and license information, please view the LICENSE
+ * file that was distributed with this source code.
+ */
+
+namespace Symfony\Component\WebLink;
+
+use Psr\Link\EvolvableLinkProviderInterface;
+use Psr\Link\LinkInterface;
+
+class GenericLinkProvider implements EvolvableLinkProviderInterface
+{
+    /**
+     * @var LinkInterface[]
+     */
+    private $links = [];
+
+    /**
+     * @param LinkInterface[] $links
+     */
+    public function __construct(array $links = [])
+    {
+        $that = $this;
+
+        foreach ($links as $link) {
+            $that = $that->withLink($link);
+        }
+
+        $this->links = $that->links;
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function getLinks(): array
+    {
+        return array_values($this->links);
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function getLinksByRel($rel): array
+    {
+        $links = [];
+
+        foreach ($this->links as $link) {
+            if (\in_array($rel, $link->getRels())) {
+                $links[] = $link;
+            }
+        }
+
+        return $links;
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function withLink(LinkInterface $link)
+    {
+        $that = clone $this;
+        $that->links[spl_object_id($link)] = $link;
+
+        return $that;
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function withoutLink(LinkInterface $link)
+    {
+        $that = clone $this;
+        unset($that->links[spl_object_id($link)]);
+
+        return $that;
+    }
+}
diff --git a/src/Symfony/Component/WebLink/Link.php b/src/Symfony/Component/WebLink/Link.php
new file mode 100644
index 000000000000..a7d034c1fae8
--- /dev/null
+++ b/src/Symfony/Component/WebLink/Link.php
@@ -0,0 +1,153 @@
+<?php
+
+/*
+ * This file is part of the Symfony package.
+ *
+ * (c) Fabien Potencier <fabien@symfony.com>
+ *
+ * For the full copyright and license information, please view the LICENSE
+ * file that was distributed with this source code.
+ */
+
+namespace Symfony\Component\WebLink;
+
+use Psr\Link\EvolvableLinkInterface;
+
+class Link implements EvolvableLinkInterface
+{
+    // Relations defined in https://www.w3.org/TR/html5/links.html#links and applicable on link elements
+    public const REL_ALTERNATE = 'alternate';
+    public const REL_AUTHOR = 'author';
+    public const REL_HELP = 'help';
+    public const REL_ICON = 'icon';
+    public const REL_LICENSE = 'license';
+    public const REL_SEARCH = 'search';
+    public const REL_STYLESHEET = 'stylesheet';
+    public const REL_NEXT = 'next';
+    public const REL_PREV = 'prev';
+
+    // Relation defined in https://www.w3.org/TR/preload/
+    public const REL_PRELOAD = 'preload';
+
+    // Relations defined in https://www.w3.org/TR/resource-hints/
+    public const REL_DNS_PREFETCH = 'dns-prefetch';
+    public const REL_PRECONNECT = 'preconnect';
+    public const REL_PREFETCH = 'prefetch';
+    public const REL_PRERENDER = 'prerender';
+
+    // Extra relations
+    public const REL_MERCURE = 'mercure';
+
+    private $href = '';
+
+    /**
+     * @var string[]
+     */
+    private $rel = [];
+
+    /**
+     * @var string[]
+     */
+    private $attributes = [];
+
+    public function __construct(string $rel = null, string $href = '')
+    {
+        if (null !== $rel) {
+            $this->rel[$rel] = $rel;
+        }
+        $this->href = $href;
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function getHref(): string
+    {
+        return $this->href;
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function isTemplated(): bool
+    {
+        return $this->hrefIsTemplated($this->href);
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function getRels(): array
+    {
+        return array_values($this->rel);
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function getAttributes(): array
+    {
+        return $this->attributes;
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function withHref($href)
+    {
+        $that = clone $this;
+        $that->href = $href;
+        $that->templated = $this->hrefIsTemplated($href);
+
+        return $that;
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function withRel($rel)
+    {
+        $that = clone $this;
+        $that->rel[$rel] = $rel;
+
+        return $that;
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function withoutRel($rel)
+    {
+        $that = clone $this;
+        unset($that->rel[$rel]);
+
+        return $that;
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function withAttribute($attribute, $value)
+    {
+        $that = clone $this;
+        $that->attributes[$attribute] = $value;
+
+        return $that;
+    }
+
+    /**
+     * {@inheritdoc}
+     */
+    public function withoutAttribute($attribute)
+    {
+        $that = clone $this;
+        unset($that->attributes[$attribute]);
+
+        return $that;
+    }
+
+    private function hrefIsTemplated(string $href): bool
+    {
+        return false !== strpos($href, '{') || false !== strpos($href, '}');
+    }
+}
diff --git a/src/Symfony/Component/WebLink/Tests/EventListener/AddLinkHeaderListenerTest.php b/src/Symfony/Component/WebLink/Tests/EventListener/AddLinkHeaderListenerTest.php
index a1b4a2078775..ddbbef7c263c 100644
--- a/src/Symfony/Component/WebLink/Tests/EventListener/AddLinkHeaderListenerTest.php
+++ b/src/Symfony/Component/WebLink/Tests/EventListener/AddLinkHeaderListenerTest.php
@@ -11,8 +11,6 @@
 
 namespace Symfony\Component\WebLink\Tests\EventListener;
 
-use Fig\Link\GenericLinkProvider;
-use Fig\Link\Link;
 use PHPUnit\Framework\TestCase;
 use Symfony\Component\EventDispatcher\EventSubscriberInterface;
 use Symfony\Component\HttpFoundation\Request;
@@ -20,6 +18,8 @@
 use Symfony\Component\HttpKernel\Event\ResponseEvent;
 use Symfony\Component\HttpKernel\KernelEvents;
 use Symfony\Component\WebLink\EventListener\AddLinkHeaderListener;
+use Symfony\Component\WebLink\GenericLinkProvider;
+use Symfony\Component\WebLink\Link;
 
 /**
  * @author Kévin Dunglas <dunglas@gmail.com>
diff --git a/src/Symfony/Component/WebLink/Tests/GenericLinkProviderTest.php b/src/Symfony/Component/WebLink/Tests/GenericLinkProviderTest.php
new file mode 100644
index 000000000000..b4176fe7f7b5
--- /dev/null
+++ b/src/Symfony/Component/WebLink/Tests/GenericLinkProviderTest.php
@@ -0,0 +1,87 @@
+<?php
+
+/*
+ * This file is part of the Symfony package.
+ *
+ * (c) Fabien Potencier <fabien@symfony.com>
+ *
+ * For the full copyright and license information, please view the LICENSE
+ * file that was distributed with this source code.
+ */
+
+namespace Symfony\Component\WebLink\Tests;
+
+use PHPUnit\Framework\TestCase;
+use Symfony\Component\WebLink\GenericLinkProvider;
+use Symfony\Component\WebLink\Link;
+
+/**
+ * Test case borrowed from https://github.com/php-fig/link/.
+ */
+class GenericLinkProviderTest extends TestCase
+{
+    public function testCanAddLinksByMethod()
+    {
+        $link = (new Link())
+            ->withHref('http://www.google.com')
+            ->withRel('next')
+            ->withAttribute('me', 'you')
+        ;
+
+        $provider = (new GenericLinkProvider())
+            ->withLink($link);
+
+        $this->assertContains($link, $provider->getLinks());
+    }
+
+    public function testCanAddLinksByConstructor()
+    {
+        $link = (new Link())
+            ->withHref('http://www.google.com')
+            ->withRel('next')
+            ->withAttribute('me', 'you')
+        ;
+
+        $provider = (new GenericLinkProvider())
+            ->withLink($link);
+
+        $this->assertContains($link, $provider->getLinks());
+    }
+
+    public function testCanGetLinksByRel()
+    {
+        $link1 = (new Link())
+            ->withHref('http://www.google.com')
+            ->withRel('next')
+            ->withAttribute('me', 'you')
+        ;
+        $link2 = (new Link())
+            ->withHref('http://www.php-fig.org/')
+            ->withRel('home')
+            ->withAttribute('me', 'you')
+        ;
+
+        $provider = (new GenericLinkProvider())
+            ->withLink($link1)
+            ->withLink($link2);
+
+        $links = $provider->getLinksByRel('home');
+        $this->assertContains($link2, $links);
+        $this->assertNotContains($link1, $links);
+    }
+
+    public function testCanRemoveLinks()
+    {
+        $link = (new Link())
+            ->withHref('http://www.google.com')
+            ->withRel('next')
+            ->withAttribute('me', 'you')
+        ;
+
+        $provider = (new GenericLinkProvider())
+            ->withLink($link)
+            ->withoutLink($link);
+
+        $this->assertNotContains($link, $provider->getLinks());
+    }
+}
diff --git a/src/Symfony/Component/WebLink/Tests/HttpHeaderSerializerTest.php b/src/Symfony/Component/WebLink/Tests/HttpHeaderSerializerTest.php
index 5347528ae02e..fa50645a7251 100644
--- a/src/Symfony/Component/WebLink/Tests/HttpHeaderSerializerTest.php
+++ b/src/Symfony/Component/WebLink/Tests/HttpHeaderSerializerTest.php
@@ -11,9 +11,9 @@
 
 namespace Symfony\Component\WebLink\Tests;
 
-use Fig\Link\Link;
 use PHPUnit\Framework\TestCase;
 use Symfony\Component\WebLink\HttpHeaderSerializer;
+use Symfony\Component\WebLink\Link;
 
 class HttpHeaderSerializerTest extends TestCase
 {
diff --git a/src/Symfony/Component/WebLink/Tests/LinkTest.php b/src/Symfony/Component/WebLink/Tests/LinkTest.php
new file mode 100644
index 000000000000..979bbb8b4f67
--- /dev/null
+++ b/src/Symfony/Component/WebLink/Tests/LinkTest.php
@@ -0,0 +1,109 @@
+<?php
+
+/*
+ * This file is part of the Symfony package.
+ *
+ * (c) Fabien Potencier <fabien@symfony.com>
+ *
+ * For the full copyright and license information, please view the LICENSE
+ * file that was distributed with this source code.
+ */
+
+namespace Symfony\Component\WebLink\Tests;
+
+use PHPUnit\Framework\TestCase;
+use Symfony\Component\WebLink\Link;
+
+/**
+ * Test case borrowed from https://github.com/php-fig/link/.
+ */
+class LinkTest extends TestCase
+{
+    public function testCanSetAndRetrieveValues()
+    {
+        $link = (new Link())
+            ->withHref('http://www.google.com')
+            ->withRel('next')
+            ->withAttribute('me', 'you')
+        ;
+
+        $this->assertEquals('http://www.google.com', $link->getHref());
+        $this->assertContains('next', $link->getRels());
+        $this->assertArrayHasKey('me', $link->getAttributes());
+        $this->assertEquals('you', $link->getAttributes()['me']);
+    }
+
+    public function testCanRemoveValues()
+    {
+        $link = (new Link())
+            ->withHref('http://www.google.com')
+            ->withRel('next')
+            ->withAttribute('me', 'you')
+        ;
+
+        $link = $link->withoutAttribute('me')
+            ->withoutRel('next');
+
+        $this->assertEquals('http://www.google.com', $link->getHref());
+        $this->assertFalse(\in_array('next', $link->getRels()));
+        $this->assertArrayNotHasKey('me', $link->getAttributes());
+    }
+
+    public function testMultipleRels()
+    {
+        $link = (new Link())
+            ->withHref('http://www.google.com')
+            ->withRel('next')
+            ->withRel('reference');
+
+        $this->assertCount(2, $link->getRels());
+        $this->assertContains('next', $link->getRels());
+        $this->assertContains('reference', $link->getRels());
+    }
+
+    public function testConstructor()
+    {
+        $link = new Link('next', 'http://www.google.com');
+
+        $this->assertEquals('http://www.google.com', $link->getHref());
+        $this->assertContains('next', $link->getRels());
+    }
+
+    /**
+     * @dataProvider templatedHrefProvider
+     */
+    public function testTemplated(string $href)
+    {
+        $link = (new Link())
+            ->withHref($href);
+
+        $this->assertTrue($link->isTemplated());
+    }
+
+    /**
+     * @dataProvider notTemplatedHrefProvider
+     */
+    public function testNotTemplated(string $href)
+    {
+        $link = (new Link())
+            ->withHref($href);
+
+        $this->assertFalse($link->isTemplated());
+    }
+
+    public function templatedHrefProvider()
+    {
+        return [
+            ['http://www.google.com/{param}/foo'],
+            ['http://www.google.com/foo?q={param}'],
+        ];
+    }
+
+    public function notTemplatedHrefProvider()
+    {
+        return [
+            ['http://www.google.com/foo'],
+            ['/foo/bar/baz'],
+        ];
+    }
+}
diff --git a/src/Symfony/Component/WebLink/composer.json b/src/Symfony/Component/WebLink/composer.json
index ba0042356571..87eccfbffa08 100644
--- a/src/Symfony/Component/WebLink/composer.json
+++ b/src/Symfony/Component/WebLink/composer.json
@@ -15,10 +15,13 @@
             "homepage": "https://symfony.com/contributors"
         }
     ],
+    "provide": {
+        "psr/link-implementation": "1.0"
+    },
     "require": {
         "php": "^7.1.3",
-        "fig/link-util": "^1.0",
-        "psr/link": "^1.0"
+        "psr/link": "^1.0",
+        "symfony/polyfill-php72": "^1.5"
     },
     "suggest": {
         "symfony/http-kernel": ""