diff --git a/recipes/openssl/1.x.x/conanfile.py b/recipes/openssl/1.x.x/conanfile.py
index 508017cfc2e5b..598230b0d5cf4 100644
--- a/recipes/openssl/1.x.x/conanfile.py
+++ b/recipes/openssl/1.x.x/conanfile.py
@@ -293,6 +293,7 @@ def _asm_target(self):
     def _targets(self):
         is_cygwin = self.settings.get_safe("os.subsystem") == "cygwin"
         is_1_0 = self._full_version < "1.1.0"
+        has_darwin_arm = self._full_version >= "1.1.1i" or is_1_0
         return {
             "Linux-x86-clang": ("%slinux-generic32" % self._target_prefix) if is_1_0 else "linux-x86-clang",
             "Linux-x86_64-clang": ("%slinux-x86_64" % self._target_prefix) if is_1_0 else "linux-x86_64-clang",
@@ -329,6 +330,7 @@ def _targets(self):
             "Macos-ppc32be-*": "%sdarwin-ppc-cc" % self._target_prefix,
             "Macos-ppc64-*": "darwin64-ppc-cc",
             "Macos-ppc64be-*": "darwin64-ppc-cc",
+            "Macos-armv8-*": "darwin64-arm64-cc" if has_darwin_arm else "darwin-common",
             "Macos-*-*": "darwin-common",
             "iOS-x86_64-*": "darwin64-x86_64-cc",
             "iOS-*-*": "iphoneos-cross",
@@ -725,6 +727,9 @@ def build(self):
                                     base_path=self._source_subfolder)
                     self._create_targets()
                 else:
+                    if self.settings.os == "Macos":
+                        tools.patch(patch_file=os.path.join("patches", "1.0.2u-darwin-arm64.patch"),
+                                    base_path=self._source_subfolder)
                     self._patch_configure()
                     self._patch_makefile_org()
                 with self._make_context():
diff --git a/recipes/openssl/1.x.x/patches/1.0.2u-darwin-arm64.patch b/recipes/openssl/1.x.x/patches/1.0.2u-darwin-arm64.patch
new file mode 100644
index 0000000000000..f04fd91d793b2
--- /dev/null
+++ b/recipes/openssl/1.x.x/patches/1.0.2u-darwin-arm64.patch
@@ -0,0 +1,12 @@
+--- Configure	2019-12-20 14:02:41.000000000 +0100
++++ Configure	2020-11-22 16:23:13.000000000 +0100
+@@ -650,7 +650,9 @@
+ "darwin-i386-cc","cc:-arch i386 -O3 -fomit-frame-pointer -DL_ENDIAN::-D_REENTRANT:MACOSX:-Wl,-search_paths_first%:BN_LLONG RC4_INT RC4_CHUNK DES_UNROLL BF_PTR:".eval{my $asm=$x86_asm;$asm=~s/cast\-586\.o//;$asm}.":macosx:dlfcn:darwin-shared:-fPIC -fno-common:-arch i386 -dynamiclib:.\$(SHLIB_MAJOR).\$(SHLIB_MINOR).dylib",
+ "debug-darwin-i386-cc","cc:-arch i386 -g3 -DL_ENDIAN::-D_REENTRANT:MACOSX:-Wl,-search_paths_first%:BN_LLONG RC4_INT RC4_CHUNK DES_UNROLL BF_PTR:${x86_asm}:macosx:dlfcn:darwin-shared:-fPIC -fno-common:-arch i386 -dynamiclib:.\$(SHLIB_MAJOR).\$(SHLIB_MINOR).dylib",
+ "darwin64-x86_64-cc","cc:-arch x86_64 -O3 -DL_ENDIAN -Wall::-D_REENTRANT:MACOSX:-Wl,-search_paths_first%:SIXTY_FOUR_BIT_LONG RC4_CHUNK DES_INT DES_UNROLL:".eval{my $asm=$x86_64_asm;$asm=~s/rc4\-[^:]+//;$asm}.":macosx:dlfcn:darwin-shared:-fPIC -fno-common:-arch x86_64 -dynamiclib:.\$(SHLIB_MAJOR).\$(SHLIB_MINOR).dylib",
++"darwin64-arm64-cc","cc:-arch arm64 -O3 -DL_ENDIAN -Wall::-D_REENTRANT:MACOSX:-Wl,-search_paths_first%:SIXTY_FOUR_BIT_LONG RC4_CHUNK DES_INT DES_UNROLL:${no_asm}:dlfcn:darwin-shared:-fPIC -fno-common:-arch arm64 -dynamiclib:.\$(SHLIB_MAJOR).\$(SHLIB_MINOR).dylib",
+ "debug-darwin64-x86_64-cc","cc:-arch x86_64 -ggdb -g2 -O0 -DL_ENDIAN -Wall::-D_REENTRANT:MACOSX:-Wl,-search_paths_first%:SIXTY_FOUR_BIT_LONG RC4_CHUNK DES_INT DES_UNROLL:".eval{my $asm=$x86_64_asm;$asm=~s/rc4\-[^:]+//;$asm}.":macosx:dlfcn:darwin-shared:-fPIC -fno-common:-arch x86_64 -dynamiclib:.\$(SHLIB_MAJOR).\$(SHLIB_MINOR).dylib",
++"debug-darwin64-arm64-cc","cc:-arch arm64 -ggdb -g2 -O0 -DL_ENDIAN -Wall::-D_REENTRANT:MACOSX:-Wl,-search_paths_first%:SIXTY_FOUR_BIT_LONG RC4_CHUNK DES_INT DES_UNROLL:${no_asm}:dlfcn:darwin-shared:-fPIC -fno-common:-arch arm64 -dynamiclib:.\$(SHLIB_MAJOR).\$(SHLIB_MINOR).dylib",
+ "debug-darwin-ppc-cc","cc:-DBN_DEBUG -DREF_CHECK -DCONF_DEBUG -DCRYPTO_MDEBUG -DB_ENDIAN -g -Wall -O::-D_REENTRANT:MACOSX::BN_LLONG RC4_CHAR RC4_CHUNK DES_UNROLL BF_PTR:${ppc32_asm}:osx32:dlfcn:darwin-shared:-fPIC:-dynamiclib:.\$(SHLIB_MAJOR).\$(SHLIB_MINOR).dylib",
+ # iPhoneOS/iOS
+ "iphoneos-cross","llvm-gcc:-O3 -isysroot \$(CROSS_TOP)/SDKs/\$(CROSS_SDK) -fomit-frame-pointer -fno-common::-D_REENTRANT:iOS:-Wl,-search_paths_first%:BN_LLONG RC4_CHAR RC4_CHUNK DES_UNROLL BF_PTR:${no_asm}:dlfcn:darwin-shared:-fPIC -fno-common:-dynamiclib:.\$(SHLIB_MAJOR).\$(SHLIB_MINOR).dylib",