diff --git a/src/material/schematics/ng-generate/mdc-migration/index.ts b/src/material/schematics/ng-generate/mdc-migration/index.ts
index 62d9c28fa7e6..a9cefd662b6d 100644
--- a/src/material/schematics/ng-generate/mdc-migration/index.ts
+++ b/src/material/schematics/ng-generate/mdc-migration/index.ts
@@ -21,6 +21,7 @@ import {RuntimeCodeMigration} from './rules/ts-migration/runtime-migration';
 import {Schema} from './schema';
 import {TemplateMigration} from './rules/template-migration';
 import {ThemingStylesMigration} from './rules/theming-styles';
+import {TypographyHierarchyTemplateMigrator} from './rules/components/typography-hierarchy/typography-hierarchy-template';
 
 /** Groups of components that must be migrated together. */
 const migrationGroups = [
@@ -44,6 +45,12 @@ const migrationGroups = [
   ['tooltip'],
 ];
 
+const TYPOGRAPHY_HIERARCHY_MIGRATOR: ComponentMigrator = {
+  component: 'typography-hierarchy',
+  template: new TypographyHierarchyTemplateMigrator(),
+  styles: null!, // TODO
+};
+
 function getComponentsToMigrate(requested: string[]): Set<string> {
   const componentsToMigrate = new Set<string>(requested);
   if (componentsToMigrate.has('all')) {
@@ -94,7 +101,10 @@ export default function (options: Schema): Rule {
     const fileSystem = new DevkitFileSystem(tree);
     const analyzedFiles = new Set<WorkspacePath>();
     const componentsToMigrate = getComponentsToMigrate(options.components);
-    const migrators = MIGRATORS.filter(m => componentsToMigrate.has(m.component));
+    const migrators = MIGRATORS.filter(m => componentsToMigrate.has(m.component)).concat(
+      // The typography hierarchy should always be migrated.
+      TYPOGRAPHY_HIERARCHY_MIGRATOR,
+    );
     let success = true;
 
     if (options.directory) {
diff --git a/src/material/schematics/ng-generate/mdc-migration/rules/components/typography-hierarchy/constants.ts b/src/material/schematics/ng-generate/mdc-migration/rules/components/typography-hierarchy/constants.ts
new file mode 100644
index 000000000000..e2a2ed61a8c7
--- /dev/null
+++ b/src/material/schematics/ng-generate/mdc-migration/rules/components/typography-hierarchy/constants.ts
@@ -0,0 +1,31 @@
+/**
+ * @license
+ * Copyright Google LLC All Rights Reserved.
+ *
+ * Use of this source code is governed by an MIT-style license that can be
+ * found in the LICENSE file at https://angular.io/license
+ */
+
+const mappings: [string, string][] = [
+  ['display-4', 'headline-1'],
+  ['display-3', 'headline-2'],
+  ['display-2', 'headline-3'],
+  ['display-1', 'headline-4'],
+  ['headline', 'headline-5'],
+  ['title', 'headline-6'],
+  ['subheading-2', 'subtitle-1'],
+  ['body-2', 'subtitle-2'],
+  ['subheading-1', 'body-1'],
+  ['body-1', 'body-2'],
+];
+
+/**
+ * Mapping between the renamed legacy typography levels and their new non-legacy names. Based on
+ * the mappings in `private-typography-to-2018-config` from `core/typography/_typography.scss`.
+ */
+export const RENAMED_TYPOGRAPHY_LEVELS = new Map(mappings);
+
+/** Mapping between the renamed typography CSS classes and their non-legacy equivalents. */
+export const RENAMED_TYPOGRAPHY_CLASSES = new Map(
+  mappings.map(m => ['mat-' + m[0], 'mat-' + m[1]]),
+);
diff --git a/src/material/schematics/ng-generate/mdc-migration/rules/components/typography-hierarchy/typography-hierarchy-template.spec.ts b/src/material/schematics/ng-generate/mdc-migration/rules/components/typography-hierarchy/typography-hierarchy-template.spec.ts
new file mode 100644
index 000000000000..4536c1b0958b
--- /dev/null
+++ b/src/material/schematics/ng-generate/mdc-migration/rules/components/typography-hierarchy/typography-hierarchy-template.spec.ts
@@ -0,0 +1,103 @@
+import {createTestApp, patchDevkitTreeToExposeTypeScript} from '@angular/cdk/schematics/testing';
+import {SchematicTestRunner, UnitTestTree} from '@angular-devkit/schematics/testing';
+import {createNewTestRunner, migrateComponents, TEMPLATE_FILE} from '../test-setup-helper';
+
+describe('typography hierarchy template migrator', () => {
+  let runner: SchematicTestRunner;
+  let cliAppTree: UnitTestTree;
+
+  async function runMigrationTest(oldFileContent: string, newFileContent: string) {
+    cliAppTree.overwrite(TEMPLATE_FILE, oldFileContent);
+    const tree = await migrateComponents([], runner, cliAppTree);
+    expect(tree.readContent(TEMPLATE_FILE)).toBe(newFileContent);
+  }
+
+  beforeEach(async () => {
+    runner = createNewTestRunner();
+    cliAppTree = patchDevkitTreeToExposeTypeScript(await createTestApp(runner));
+  });
+
+  it('should migrate legacy typography levels in static attributes', async () => {
+    await runMigrationTest(
+      `
+        <h1 class="mat-display-4">Hello</h1>
+        <h1 class="mat-display-3">Hello</h1>
+        <h1 class="mat-display-2">Hello</h1>
+        <h1 class="mat-display-1">Hello</h1>
+        <h1 class="mat-headline">Hello</h1>
+        <h1 class="mat-title">Hello</h1>
+        <h1 class="mat-subheading-2">Hello</h1>
+        <h1 class="mat-body-2">Hello</h1>
+        <h1 class="mat-subheading-1">Hello</h1>
+        <h1 class="mat-body-1">Hello</h1>
+      `,
+      `
+        <h1 class="mat-headline-1">Hello</h1>
+        <h1 class="mat-headline-2">Hello</h1>
+        <h1 class="mat-headline-3">Hello</h1>
+        <h1 class="mat-headline-4">Hello</h1>
+        <h1 class="mat-headline-5">Hello</h1>
+        <h1 class="mat-headline-6">Hello</h1>
+        <h1 class="mat-subtitle-1">Hello</h1>
+        <h1 class="mat-subtitle-2">Hello</h1>
+        <h1 class="mat-body-1">Hello</h1>
+        <h1 class="mat-body-2">Hello</h1>
+      `,
+    );
+  });
+
+  it('should migrate multiple static class usages of the legacy typography levels in a single file', async () => {
+    await runMigrationTest(
+      `
+        <h1 class="header mat-display-4" other-attr="foo">Hello</h1><div foo="bar"></div>
+        <h2 class="mat-display-3">Hi</h2>
+      `,
+      `
+        <h1 class="header mat-headline-1" other-attr="foo">Hello</h1><div foo="bar"></div>
+        <h2 class="mat-headline-2">Hi</h2>
+      `,
+    );
+  });
+
+  it('should migrate legacy typography levels in class bindings', async () => {
+    await runMigrationTest(
+      `
+        <h1 [class.mat-display-4]="expr">Hello</h1>
+        <h1 [class.mat-display-3]="expr">Hello</h1>
+        <h1 [class.mat-display-2]="expr">Hello</h1>
+        <h1 [class.mat-display-1]="expr">Hello</h1>
+        <h1 [class.mat-headline]="expr">Hello</h1>
+        <h1 [class.mat-title]="expr">Hello</h1>
+        <h1 [class.mat-subheading-2]="expr">Hello</h1>
+        <h1 [class.mat-body-2]="expr">Hello</h1>
+        <h1 [class.mat-subheading-1]="expr">Hello</h1>
+        <h1 [class.mat-body-1]="expr">Hello</h1>
+      `,
+      `
+        <h1 [class.mat-headline-1]="expr">Hello</h1>
+        <h1 [class.mat-headline-2]="expr">Hello</h1>
+        <h1 [class.mat-headline-3]="expr">Hello</h1>
+        <h1 [class.mat-headline-4]="expr">Hello</h1>
+        <h1 [class.mat-headline-5]="expr">Hello</h1>
+        <h1 [class.mat-headline-6]="expr">Hello</h1>
+        <h1 [class.mat-subtitle-1]="expr">Hello</h1>
+        <h1 [class.mat-subtitle-2]="expr">Hello</h1>
+        <h1 [class.mat-body-1]="expr">Hello</h1>
+        <h1 [class.mat-body-2]="expr">Hello</h1>
+      `,
+    );
+  });
+
+  it('should migrate mixed class bindings and static class attribute', async () => {
+    await runMigrationTest(
+      `
+        <h1 [class.mat-display-4]="someExpr" class="foo mat-subheading-2 bar">Hello</h1>
+        <h1 [class.mat-display-1]="someExpr">Hello</h1>
+      `,
+      `
+        <h1 [class.mat-headline-1]="someExpr" class="foo mat-subtitle-1 bar">Hello</h1>
+        <h1 [class.mat-headline-4]="someExpr">Hello</h1>
+      `,
+    );
+  });
+});
diff --git a/src/material/schematics/ng-generate/mdc-migration/rules/components/typography-hierarchy/typography-hierarchy-template.ts b/src/material/schematics/ng-generate/mdc-migration/rules/components/typography-hierarchy/typography-hierarchy-template.ts
new file mode 100644
index 000000000000..d98194768661
--- /dev/null
+++ b/src/material/schematics/ng-generate/mdc-migration/rules/components/typography-hierarchy/typography-hierarchy-template.ts
@@ -0,0 +1,72 @@
+/**
+ * @license
+ * Copyright Google LLC All Rights Reserved.
+ *
+ * Use of this source code is governed by an MIT-style license that can be
+ * found in the LICENSE file at https://angular.io/license
+ */
+
+import * as compiler from '@angular/compiler';
+import {TemplateMigrator} from '../../template-migrator';
+import {visitElements} from '../../tree-traversal';
+import {Update} from '../../../../../migration-utilities';
+import {RENAMED_TYPOGRAPHY_CLASSES} from './constants';
+
+export class TypographyHierarchyTemplateMigrator extends TemplateMigrator {
+  getUpdates(ast: compiler.ParsedTemplate): Update[] {
+    const updates: Update[] = [];
+
+    visitElements(ast.nodes, node => {
+      this._addStaticClassUpdates(node, updates);
+      this._addClassBindingUpdates(node, updates);
+    });
+
+    return updates;
+  }
+
+  /** Migrates the legacy typography classes in a static `class` attribute. */
+  private _addStaticClassUpdates(node: compiler.TmplAstElement, updates: Update[]): void {
+    const classAttr = node.attributes.find(attr => attr.name === 'class');
+
+    if (classAttr && classAttr.keySpan && classAttr.valueSpan && classAttr.value.includes('mat-')) {
+      const classes = classAttr.value.split(' ');
+      let hasChanged = false;
+
+      classes.forEach((current, index) => {
+        if (RENAMED_TYPOGRAPHY_CLASSES.has(current)) {
+          hasChanged = true;
+          classes[index] = RENAMED_TYPOGRAPHY_CLASSES.get(current)!;
+        }
+      });
+
+      if (hasChanged) {
+        updates.push({
+          offset: classAttr.keySpan.start.offset,
+          updateFn: html =>
+            html.slice(0, classAttr.valueSpan!.start.offset) +
+            classes.join(' ') +
+            html.slice(classAttr.valueSpan!.end.offset),
+        });
+      }
+    }
+  }
+
+  /** Migrates the legacy typography classes in `[class.x]` bindings. */
+  private _addClassBindingUpdates(node: compiler.TmplAstElement, updates: Update[]): void {
+    node.inputs.forEach(input => {
+      if (input.type === compiler.BindingType.Class && RENAMED_TYPOGRAPHY_CLASSES.has(input.name)) {
+        updates.push({
+          offset: input.keySpan.start.offset,
+          updateFn: html => {
+            return (
+              html.slice(0, input.keySpan.start.offset) +
+              'class.' +
+              RENAMED_TYPOGRAPHY_CLASSES.get(input.name)! +
+              html.slice(input.keySpan.end.offset)
+            );
+          },
+        });
+      }
+    });
+  }
+}
diff --git a/src/material/schematics/ng-generate/mdc-migration/rules/theming-styles.ts b/src/material/schematics/ng-generate/mdc-migration/rules/theming-styles.ts
index 6a9f7ce35ac3..1313475ed632 100644
--- a/src/material/schematics/ng-generate/mdc-migration/rules/theming-styles.ts
+++ b/src/material/schematics/ng-generate/mdc-migration/rules/theming-styles.ts
@@ -11,26 +11,10 @@ import {SchematicContext} from '@angular-devkit/schematics';
 import * as postcss from 'postcss';
 import * as scss from 'postcss-scss';
 import {ComponentMigrator, MIGRATORS} from '.';
+import {RENAMED_TYPOGRAPHY_LEVELS} from './components/typography-hierarchy/constants';
 
 const COMPONENTS_MIXIN_NAME = /\.([^(;]*)/;
 
-/**
- * Mapping between the renamed legacy typography levels and their new non-legacy names. Based on
- * the mappings in `private-typography-to-2018-config` from `core/typography/_typography.scss`.
- */
-const RENAMED_TYPOGRAPHY_LEVELS = new Map([
-  ['display-4', 'headline-1'],
-  ['display-3', 'headline-2'],
-  ['display-2', 'headline-3'],
-  ['display-1', 'headline-4'],
-  ['headline', 'headline-5'],
-  ['title', 'headline-6'],
-  ['subheading-2', 'subtitle-1'],
-  ['body-2', 'subtitle-2'],
-  ['subheading-1', 'body-1'],
-  ['body-1', 'body-2'],
-]);
-
 export class ThemingStylesMigration extends Migration<ComponentMigrator[], SchematicContext> {
   enabled = true;
   private _namespace: string;