diff --git a/packages/block-library/src/editor.scss b/packages/block-library/src/editor.scss
index c945e2bf99a70a..8f232cb0a35e6f 100644
--- a/packages/block-library/src/editor.scss
+++ b/packages/block-library/src/editor.scss
@@ -17,6 +17,7 @@
 @import "./classic/editor.scss";
 @import "./gallery/editor.scss";
 @import "./group/editor.scss";
+@import "./heading/editor.scss";
 @import "./html/editor.scss";
 @import "./image/editor.scss";
 @import "./latest-comments/editor.scss";
diff --git a/packages/block-library/src/heading/edit.js b/packages/block-library/src/heading/edit.js
index 524eee735b57c9..d4a353c1b0ead4 100644
--- a/packages/block-library/src/heading/edit.js
+++ b/packages/block-library/src/heading/edit.js
@@ -3,25 +3,23 @@
  */
 import classnames from 'classnames';
 
-/**
- * Internal dependencies
- */
-import HeadingToolbar from './heading-toolbar';
-
 /**
  * WordPress dependencies
  */
 import { __ } from '@wordpress/i18n';
-import { PanelBody, __experimentalText as Text } from '@wordpress/components';
 import { createBlock } from '@wordpress/blocks';
 import {
 	AlignmentToolbar,
 	BlockControls,
-	InspectorControls,
 	RichText,
 	__experimentalBlock as Block,
 } from '@wordpress/block-editor';
-import { Platform } from '@wordpress/element';
+import { ToolbarGroup } from '@wordpress/components';
+
+/**
+ * Internal dependencies
+ */
+import HeadingLevelDropdown from './heading-level-dropdown';
 
 function HeadingEdit( {
 	attributes,
@@ -36,14 +34,14 @@ function HeadingEdit( {
 	return (
 		<>
 			<BlockControls>
-				<HeadingToolbar
-					minLevel={ Platform.OS === 'web' ? 2 : 1 }
-					maxLevel={ Platform.OS === 'web' ? 5 : 7 }
-					selectedLevel={ level }
-					onChange={ ( newLevel ) =>
-						setAttributes( { level: newLevel } )
-					}
-				/>
+				<ToolbarGroup>
+					<HeadingLevelDropdown
+						selectedLevel={ level }
+						onChange={ ( newLevel ) =>
+							setAttributes( { level: newLevel } )
+						}
+					/>
+				</ToolbarGroup>
 				<AlignmentToolbar
 					value={ align }
 					onChange={ ( nextAlign ) => {
@@ -51,22 +49,6 @@ function HeadingEdit( {
 					} }
 				/>
 			</BlockControls>
-			{ Platform.OS === 'web' && (
-				<InspectorControls>
-					<PanelBody title={ __( 'Heading settings' ) }>
-						<Text variant="label">{ __( 'Level' ) }</Text>
-						<HeadingToolbar
-							isCollapsed={ false }
-							minLevel={ 1 }
-							maxLevel={ 7 }
-							selectedLevel={ level }
-							onChange={ ( newLevel ) =>
-								setAttributes( { level: newLevel } )
-							}
-						/>
-					</PanelBody>
-				</InspectorControls>
-			) }
 			<RichText
 				identifier="content"
 				tagName={ Block[ tagName ] }
diff --git a/packages/block-library/src/heading/editor.scss b/packages/block-library/src/heading/editor.scss
new file mode 100644
index 00000000000000..522266d9a9a9e3
--- /dev/null
+++ b/packages/block-library/src/heading/editor.scss
@@ -0,0 +1,14 @@
+// Remove padding in heading level control popover since the toolbar buttons already have padding.
+.block-library-heading-level-dropdown .components-popover__content {
+	padding: 0;
+	// TODO: Find a less hardcoded way of doing this. `max-content` works on
+	// Chromium, but it results in a scrollbar on Safari, and isn't supported
+	// at all in IE11.
+	min-width: 230px;
+}
+
+// The dropdown already has a border, so we can remove the one on the heading
+// level toolbar.
+.block-library-heading-level-toolbar {
+	border: none;
+}
diff --git a/packages/block-library/src/heading/heading-level-dropdown.js b/packages/block-library/src/heading/heading-level-dropdown.js
new file mode 100644
index 00000000000000..5039a30217656d
--- /dev/null
+++ b/packages/block-library/src/heading/heading-level-dropdown.js
@@ -0,0 +1,112 @@
+/**
+ * WordPress dependencies
+ */
+import {
+	Dropdown,
+	Toolbar,
+	ToolbarButton,
+	ToolbarGroup,
+} from '@wordpress/components';
+import { __, sprintf } from '@wordpress/i18n';
+import { DOWN } from '@wordpress/keycodes';
+
+/**
+ * Internal dependencies
+ */
+import HeadingLevelIcon from './heading-level-icon';
+
+const HEADING_LEVELS = [ 1, 2, 3, 4, 5, 6 ];
+
+const POPOVER_PROPS = {
+	className: 'block-library-heading-level-dropdown',
+	isAlternate: true,
+};
+
+/** @typedef {import('@wordpress/element').WPComponent} WPComponent */
+
+/**
+ * HeadingLevelDropdown props.
+ *
+ * @typedef WPHeadingLevelDropdownProps
+ *
+ * @property {number}                 selectedLevel The chosen heading level.
+ * @property {(newValue:number)=>any} onChange      Callback to run when
+ *                                                  toolbar value is changed.
+ */
+
+/**
+ * Dropdown for selecting a heading level (1 through 6).
+ *
+ * @param {WPHeadingLevelDropdownProps} props Component props.
+ *
+ * @return {WPComponent} The toolbar.
+ */
+export default function HeadingLevelDropdown( { selectedLevel, onChange } ) {
+	return (
+		<Dropdown
+			popoverProps={ POPOVER_PROPS }
+			renderToggle={ ( { onToggle, isOpen } ) => {
+				const openOnArrowDown = ( event ) => {
+					if ( ! isOpen && event.keyCode === DOWN ) {
+						event.preventDefault();
+						event.stopPropagation();
+						onToggle();
+					}
+				};
+
+				return (
+					<ToolbarButton
+						aria-expanded={ isOpen }
+						aria-haspopup="true"
+						icon={ <HeadingLevelIcon level={ selectedLevel } /> }
+						label={ __( 'Change heading level' ) }
+						onClick={ onToggle }
+						onKeyDown={ openOnArrowDown }
+						showTooltip
+					/>
+				);
+			} }
+			renderContent={ () => (
+				<Toolbar
+					className="block-library-heading-level-toolbar"
+					__experimentalAccessibilityLabel={ __(
+						'Change heading level'
+					) }
+				>
+					<ToolbarGroup
+						isCollapsed={ false }
+						controls={ HEADING_LEVELS.map( ( targetLevel ) => {
+							const isActive = targetLevel === selectedLevel;
+							return {
+								icon: (
+									<HeadingLevelIcon
+										level={ targetLevel }
+										isPressed={ isActive }
+									/>
+								),
+								title: sprintf(
+									// translators: %s: heading level e.g: "1", "2", "3"
+									__( 'Heading %d' ),
+									targetLevel
+								),
+								isActive,
+								onClick() {
+									onChange( targetLevel );
+								},
+								// Temporary workaround for macOS Firefox/Safari issue
+								// where clicking buttons in the heading level toolbar
+								// doesn't work.
+								// TODO: Replace this with a more general solution.
+								// https://github.com/WordPress/gutenberg/pull/20246#pullrequestreview-417338057
+								onMouseDown( event ) {
+									event.preventDefault();
+									event.currentTarget.focus();
+								},
+							};
+						} ) }
+					/>
+				</Toolbar>
+			) }
+		/>
+	);
+}
diff --git a/packages/block-library/src/heading/heading-level-dropdown.native.js b/packages/block-library/src/heading/heading-level-dropdown.native.js
new file mode 100644
index 00000000000000..e24374c86b995c
--- /dev/null
+++ b/packages/block-library/src/heading/heading-level-dropdown.native.js
@@ -0,0 +1,63 @@
+/**
+ * WordPress dependencies
+ */
+import { __, sprintf } from '@wordpress/i18n';
+import { DropdownMenu } from '@wordpress/components';
+
+/**
+ * Internal dependencies
+ */
+import HeadingLevelIcon from './heading-level-icon';
+
+const HEADING_LEVELS = [ 1, 2, 3, 4, 5, 6 ];
+
+/** @typedef {import('@wordpress/element').WPComponent} WPComponent */
+
+/**
+ * HeadingLevelDropdown props.
+ *
+ * @typedef WPHeadingLevelDropdownProps
+ *
+ * @property {number}                 selectedLevel The chosen heading level.
+ * @property {(newValue:number)=>any} onChange      Callback to run when
+ *                                                  toolbar value is changed.
+ */
+
+/**
+ * Dropdown for selecting a heading level (1 through 6).
+ *
+ * @param {WPHeadingLevelDropdownProps} props Component props.
+ *
+ * @return {WPComponent} The toolbar.
+ */
+export default function HeadingLevelDropdown( { selectedLevel, onChange } ) {
+	const createLevelControl = (
+		targetLevel,
+		currentLevel,
+		onChangeCallback
+	) => {
+		const isActive = targetLevel === currentLevel;
+		return {
+			icon: (
+				<HeadingLevelIcon
+					level={ targetLevel }
+					isPressed={ isActive }
+				/>
+			),
+			// translators: %s: heading level e.g: "1", "2", "3"
+			title: sprintf( __( 'Heading %d' ), targetLevel ),
+			isActive,
+			onClick: () => onChangeCallback( targetLevel ),
+		};
+	};
+
+	return (
+		<DropdownMenu
+			icon={ <HeadingLevelIcon level={ selectedLevel } /> }
+			controls={ HEADING_LEVELS.map( ( index ) =>
+				createLevelControl( index, selectedLevel, onChange )
+			) }
+			label={ __( 'Change heading level' ) }
+		/>
+	);
+}
diff --git a/packages/block-library/src/heading/heading-level-icon.js b/packages/block-library/src/heading/heading-level-icon.js
index eef2b3af3b5e7e..b3288d02761612 100644
--- a/packages/block-library/src/heading/heading-level-icon.js
+++ b/packages/block-library/src/heading/heading-level-icon.js
@@ -3,6 +3,24 @@
  */
 import { Path, SVG } from '@wordpress/components';
 
+/** @typedef {import('@wordpress/element').WPComponent} WPComponent */
+
+/**
+ * HeadingLevelIcon props.
+ *
+ * @typedef WPHeadingLevelIconProps
+ *
+ * @property {number}   level     The heading level to show an icon for.
+ * @property {?boolean} isPressed Whether or not the icon should appear pressed; default: false.
+ */
+
+/**
+ * Heading level icon.
+ *
+ * @param {WPHeadingLevelIconProps} props Component props.
+ *
+ * @return {?WPComponent} The icon.
+ */
 export default function HeadingLevelIcon( { level, isPressed = false } ) {
 	const levelToPath = {
 		1: 'M9 5h2v10H9v-4H5v4H3V5h2v4h4V5zm6.6 0c-.6.9-1.5 1.7-2.6 2v1h2v7h2V5h-1.4z',
diff --git a/packages/block-library/src/heading/heading-toolbar.js b/packages/block-library/src/heading/heading-toolbar.js
deleted file mode 100644
index 97cd4f12cfe23c..00000000000000
--- a/packages/block-library/src/heading/heading-toolbar.js
+++ /dev/null
@@ -1,57 +0,0 @@
-/**
- * External dependencies
- */
-import { range } from 'lodash';
-
-/**
- * WordPress dependencies
- */
-import { __, sprintf } from '@wordpress/i18n';
-import { Component } from '@wordpress/element';
-import { ToolbarGroup } from '@wordpress/components';
-
-/**
- * Internal dependencies
- */
-import HeadingLevelIcon from './heading-level-icon';
-
-class HeadingToolbar extends Component {
-	createLevelControl( targetLevel, selectedLevel, onChange ) {
-		const isActive = targetLevel === selectedLevel;
-		return {
-			icon: (
-				<HeadingLevelIcon
-					level={ targetLevel }
-					isPressed={ isActive }
-				/>
-			),
-			// translators: %s: heading level e.g: "1", "2", "3"
-			title: sprintf( __( 'Heading %d' ), targetLevel ),
-			isActive,
-			onClick: () => onChange( targetLevel ),
-		};
-	}
-
-	render() {
-		const {
-			isCollapsed = true,
-			minLevel,
-			maxLevel,
-			selectedLevel,
-			onChange,
-		} = this.props;
-
-		return (
-			<ToolbarGroup
-				isCollapsed={ isCollapsed }
-				icon={ <HeadingLevelIcon level={ selectedLevel } /> }
-				controls={ range( minLevel, maxLevel ).map( ( index ) =>
-					this.createLevelControl( index, selectedLevel, onChange )
-				) }
-				label={ __( 'Change heading level' ) }
-			/>
-		);
-	}
-}
-
-export default HeadingToolbar;
diff --git a/packages/components/src/index.native.js b/packages/components/src/index.native.js
index bae36d9885b452..4168d198185ea4 100644
--- a/packages/components/src/index.native.js
+++ b/packages/components/src/index.native.js
@@ -12,6 +12,7 @@ export { default as ColorIndicator } from './color-indicator';
 export { default as ColorPalette } from './color-palette';
 export { default as Dashicon } from './dashicon';
 export { default as Dropdown } from './dropdown';
+export { default as DropdownMenu } from './dropdown-menu';
 export { default as Toolbar } from './toolbar';
 export { default as ToolbarButton } from './toolbar-button';
 export { default as __experimentalToolbarContext } from './toolbar-context';
diff --git a/packages/e2e-tests/specs/editor/various/rich-text.test.js b/packages/e2e-tests/specs/editor/various/rich-text.test.js
index 8135962e22556e..1ac2080a1631cb 100644
--- a/packages/e2e-tests/specs/editor/various/rich-text.test.js
+++ b/packages/e2e-tests/specs/editor/various/rich-text.test.js
@@ -7,7 +7,6 @@ import {
 	insertBlock,
 	clickBlockAppender,
 	pressKeyWithModifier,
-	openDocumentSettingsSidebar,
 } from '@wordpress/e2e-test-utils';
 
 describe( 'RichText', () => {
@@ -23,7 +22,8 @@ describe( 'RichText', () => {
 		//
 		// See: https://github.com/WordPress/gutenberg/issues/3091
 		await insertBlock( 'Heading' );
-		await openDocumentSettingsSidebar();
+		await page.waitForSelector( '[aria-label="Change heading level"]' );
+		await page.click( '[aria-label="Change heading level"]' );
 		await page.click( '[aria-label="Heading 3"]' );
 
 		expect( await getEditedPostContent() ).toMatchSnapshot();