diff --git a/editor/components/block-settings-menu/html-converter.js b/editor/components/block-settings-menu/html-converter.js
new file mode 100644
index 00000000000000..826c5d647a687e
--- /dev/null
+++ b/editor/components/block-settings-menu/html-converter.js
@@ -0,0 +1,50 @@
+/**
+ * WordPress dependencies
+ */
+import { __ } from '@wordpress/i18n';
+import { IconButton } from '@wordpress/components';
+import { rawHandler, getBlockContent } from '@wordpress/blocks';
+import { compose } from '@wordpress/element';
+import { withSelect, withDispatch } from '@wordpress/data';
+
+export function HTMLConverter( { block, onReplace, small, canUserUseUnfilteredHTML, role } ) {
+	if ( ! block || block.name !== 'core/html' ) {
+		return null;
+	}
+
+	const label = __( 'Convert to blocks' );
+
+	const convertToBlocks = () => {
+		onReplace( block.uid, rawHandler( {
+			HTML: getBlockContent( block ),
+			mode: 'BLOCKS',
+			canUserUseUnfilteredHTML,
+		} ) );
+	};
+
+	return (
+		<IconButton
+			className="editor-block-settings-menu__control"
+			onClick={ convertToBlocks }
+			icon="screenoptions"
+			label={ small ? label : undefined }
+			role={ role }
+		>
+			{ ! small && label }
+		</IconButton>
+	);
+}
+
+export default compose(
+	withSelect( ( select, { uid } ) => {
+		const { getBlock, getCurrentPostType, canUserUseUnfilteredHTML } = select( 'core/editor' );
+		return {
+			block: getBlock( uid ),
+			postType: getCurrentPostType(),
+			canUserUseUnfilteredHTML: canUserUseUnfilteredHTML(),
+		};
+	} ),
+	withDispatch( ( dispatch ) => ( {
+		onReplace: dispatch( 'core/editor' ).replaceBlocks,
+	} ) ),
+)( HTMLConverter );
diff --git a/editor/components/block-settings-menu/index.js b/editor/components/block-settings-menu/index.js
index e8fd0439e6b76b..c69ecdf0e7f698 100644
--- a/editor/components/block-settings-menu/index.js
+++ b/editor/components/block-settings-menu/index.js
@@ -22,6 +22,7 @@ import BlockRemoveButton from './block-remove-button';
 import SharedBlockConvertButton from './shared-block-convert-button';
 import SharedBlockDeleteButton from './shared-block-delete-button';
 import UnknownConverter from './unknown-converter';
+import HTMLConverter from './html-converter';
 import _BlockSettingsMenuFirstItem from './block-settings-menu-first-item';
 
 export class BlockSettingsMenu extends Component {
@@ -95,6 +96,7 @@ export class BlockSettingsMenu extends Component {
 							<_BlockSettingsMenuFirstItem.Slot fillProps={ { onClose } } />
 							{ count === 1 && <BlockModeToggle uid={ firstBlockUID } onToggle={ onClose } role="menuitem" /> }
 							{ count === 1 && <UnknownConverter uid={ firstBlockUID } role="menuitem" /> }
+							{ count === 1 && <HTMLConverter uid={ firstBlockUID } role="menuitem" /> }
 							<BlockDuplicateButton uids={ uids } rootUID={ rootUID } role="menuitem" />
 							{ count === 1 && <SharedBlockConvertButton uid={ firstBlockUID } onToggle={ onClose } itemsRole="menuitem" /> }
 							<div className="editor-block-settings-menu__separator" />
diff --git a/editor/store/selectors.js b/editor/store/selectors.js
index c1fa0e87600136..6911186833790d 100644
--- a/editor/store/selectors.js
+++ b/editor/store/selectors.js
@@ -1891,3 +1891,14 @@ export function getTokenSettings( state, name ) {
 
 	return state.tokens[ name ];
 }
+
+/**
+ * Returns whether or not the user has the unfiltered_html capability.
+ *
+ * @param {Object} state Editor state.
+ *
+ * @return {boolean} Whether the user can or can't post unfiltered HTML.
+ */
+export function canUserUseUnfilteredHTML( state ) {
+	return has( getCurrentPost( state ), [ '_links', 'wp:action-unfiltered_html' ] );
+}
diff --git a/editor/store/test/selectors.js b/editor/store/test/selectors.js
index 8bbdb1f9a2c9c3..d8cf70809c4bbf 100644
--- a/editor/store/test/selectors.js
+++ b/editor/store/test/selectors.js
@@ -16,6 +16,7 @@ import { moment } from '@wordpress/date';
 import * as selectors from '../selectors';
 
 const {
+	canUserUseUnfilteredHTML,
 	hasEditorUndo,
 	hasEditorRedo,
 	isEditedPostNew,
@@ -3809,4 +3810,25 @@ describe( 'selectors', () => {
 			expect( getBlockListSettings( state, 'chicken' ) ).toBe( undefined );
 		} );
 	} );
+
+	describe( 'canUserUseUnfilteredHTML', () => {
+		it( 'should return true if the _links object contains the property wp:action-unfiltered_html', () => {
+			const state = {
+				currentPost: {
+					_links: {
+						'wp:action-unfiltered_html': [],
+					},
+				},
+			};
+			expect( canUserUseUnfilteredHTML( state ) ).toBe( true );
+		} );
+		it( 'should return false if the _links object doesnt contain the property wp:action-unfiltered_html', () => {
+			const state = {
+				currentPost: {
+					_links: {},
+				},
+			};
+			expect( canUserUseUnfilteredHTML( state ) ).toBe( false );
+		} );
+	} );
 } );
diff --git a/lib/rest-api.php b/lib/rest-api.php
index b05e2e46abb95d..d2d08cbd824d7e 100644
--- a/lib/rest-api.php
+++ b/lib/rest-api.php
@@ -247,6 +247,22 @@ function gutenberg_add_target_schema_to_links( $response, $post, $request ) {
 			);
 		}
 	}
+	if ( 'edit' === $request['context'] && current_user_can( 'unfiltered_html' ) ) {
+		$new_links['https://api.w.org/action-unfiltered_html'] = array(
+			array(
+				'title'        => __( 'The current user can post HTML markup and JavaScript.', 'gutenberg' ),
+				'href'         => $orig_href,
+				'targetSchema' => array(
+					'type'       => 'object',
+					'properties' => array(
+						'unfiltered_html' => array(
+							'type' => 'boolean',
+						),
+					),
+				),
+			),
+		);
+	}
 	if ( 'edit' === $request['context'] ) {
 		if ( current_user_can( $post_type->cap->publish_posts ) ) {
 			$new_links['https://api.w.org/action-publish'] = array(
diff --git a/phpunit/class-gutenberg-rest-api-test.php b/phpunit/class-gutenberg-rest-api-test.php
index ad51a7ee1845f6..9b65d34d4f9489 100644
--- a/phpunit/class-gutenberg-rest-api-test.php
+++ b/phpunit/class-gutenberg-rest-api-test.php
@@ -130,6 +130,51 @@ function test_viewable_field_without_context() {
 		$this->assertFalse( isset( $result['viewable'] ) );
 	}
 
+	/**
+	 * Only returns wp:action-unfiltered_html when current user can use unfiltered HTML.
+	 * See https://codex.wordpress.org/Roles_and_Capabilities#Capability_vs._Role_Table
+	 */
+	function test_link_unfiltered_html() {
+		$post_id   = $this->factory->post->create();
+		$check_key = 'https://api.w.org/action-unfiltered_html';
+		// admins can in a single site, but can't in a multisite.
+		wp_set_current_user( $this->administrator );
+		$request = new WP_REST_Request( 'GET', '/wp/v2/posts/' . $post_id );
+		$request->set_param( 'context', 'edit' );
+		$response = rest_do_request( $request );
+		$links    = $response->get_links();
+		if ( is_multisite() ) {
+			$this->assertFalse( isset( $links[ $check_key ] ) );
+		} else {
+			$this->assertTrue( isset( $links[ $check_key ] ) );
+		}
+		// authors can't.
+		wp_set_current_user( $this->author );
+		$request = new WP_REST_Request( 'GET', '/wp/v2/posts/' . $post_id );
+		$request->set_param( 'context', 'edit' );
+		$response = rest_do_request( $request );
+		$links    = $response->get_links();
+		$this->assertFalse( isset( $links[ $check_key ] ) );
+		// editors can in a single site, but can't in a multisite.
+		wp_set_current_user( $this->editor );
+		$request = new WP_REST_Request( 'GET', '/wp/v2/posts/' . $post_id );
+		$request->set_param( 'context', 'edit' );
+		$response = rest_do_request( $request );
+		$links    = $response->get_links();
+		if ( is_multisite() ) {
+			$this->assertFalse( isset( $links[ $check_key ] ) );
+		} else {
+			$this->assertTrue( isset( $links[ $check_key ] ) );
+		}
+		// contributors can't.
+		wp_set_current_user( $this->contributor );
+		$request = new WP_REST_Request( 'GET', '/wp/v2/posts/' . $post_id );
+		$request->set_param( 'context', 'edit' );
+		$response = rest_do_request( $request );
+		$links    = $response->get_links();
+		$this->assertFalse( isset( $links[ $check_key ] ) );
+	}
+
 	/**
 	 * Only returns wp:action-assign-author when current user can assign author.
 	 */