diff --git a/packages/block-editor/src/components/block-mover/index.native.js b/packages/block-editor/src/components/block-mover/index.native.js
index aa1892c33e8042..d64509ff17726e 100644
--- a/packages/block-editor/src/components/block-mover/index.native.js
+++ b/packages/block-editor/src/components/block-mover/index.native.js
@@ -2,29 +2,52 @@
  * External dependencies
  */
 import { first, last, partial, castArray } from 'lodash';
+import { Platform } from 'react-native';
 
 /**
  * WordPress dependencies
  */
-import { ToolbarButton } from '@wordpress/components';
-import { withSelect, withDispatch } from '@wordpress/data';
+import { __ } from '@wordpress/i18n';
+import { Picker, ToolbarButton } from '@wordpress/components';
 import { withInstanceId, compose } from '@wordpress/compose';
+import { withSelect, withDispatch } from '@wordpress/data';
+import { useRef, useState } from '@wordpress/element';
 
 /**
  * Internal dependencies
  */
 import { getMoversSetup } from './mover-description';
 
-const BlockMover = ( {
+export const BLOCK_MOVER_DIRECTION_TOP = 'blockPageMoverOptions-moveToTop';
+export const BLOCK_MOVER_DIRECTION_BOTTOM =
+	'blockPageMoverOptions-moveToBottom';
+
+export const BlockMover = ( {
 	isFirst,
 	isLast,
 	isLocked,
 	onMoveDown,
 	onMoveUp,
+	onLongMove,
 	firstIndex,
+	numberOfBlocks,
 	rootClientId,
 	isStackedHorizontally,
 } ) => {
+	const pickerRef = useRef();
+	const [ blockPageMoverState, setBlockPageMoverState ] = useState(
+		undefined
+	);
+	const showBlockPageMover = ( direction ) => () => {
+		if ( ! pickerRef.current ) {
+			setBlockPageMoverState( undefined );
+			return;
+		}
+
+		setBlockPageMoverState( direction );
+		pickerRef.current.presentPicker();
+	};
+
 	const {
 		description: {
 			backwardButtonHint,
@@ -36,6 +59,32 @@ const BlockMover = ( {
 		title: { backward: backwardButtonTitle, forward: forwardButtonTitle },
 	} = getMoversSetup( isStackedHorizontally, { firstIndex } );
 
+	const blockPageMoverOptions = [
+		{
+			icon: backwardButtonIcon,
+			label: __( 'Move to top' ),
+			value: BLOCK_MOVER_DIRECTION_TOP,
+			onSelect: () => {
+				onLongMove()( 0 );
+			},
+		},
+		{
+			icon: forwardButtonIcon,
+			label: __( 'Move to bottom' ),
+			value: BLOCK_MOVER_DIRECTION_BOTTOM,
+			onSelect: () => {
+				onLongMove()( numberOfBlocks );
+			},
+		},
+	].filter( ( el ) => el.value === blockPageMoverState );
+
+	const onPickerSelect = ( value ) => {
+		const option = blockPageMoverOptions.find(
+			( el ) => el.value === value
+		);
+		if ( option && option.onSelect ) option.onSelect();
+	};
+
 	if ( isLocked || ( isFirst && isLast && ! rootClientId ) ) {
 		return null;
 	}
@@ -46,6 +95,7 @@ const BlockMover = ( {
 				title={ ! isFirst ? backwardButtonTitle : firstBlockTitle }
 				isDisabled={ isFirst }
 				onClick={ onMoveUp }
+				onLongPress={ showBlockPageMover( BLOCK_MOVER_DIRECTION_TOP ) }
 				icon={ backwardButtonIcon }
 				extraProps={ { hint: backwardButtonHint } }
 			/>
@@ -54,11 +104,23 @@ const BlockMover = ( {
 				title={ ! isLast ? forwardButtonTitle : lastBlockTitle }
 				isDisabled={ isLast }
 				onClick={ onMoveDown }
+				onLongPress={ showBlockPageMover(
+					BLOCK_MOVER_DIRECTION_BOTTOM
+				) }
 				icon={ forwardButtonIcon }
 				extraProps={ {
 					hint: forwardButtonHint,
 				} }
 			/>
+
+			<Picker
+				ref={ pickerRef }
+				options={ blockPageMoverOptions }
+				onChange={ onPickerSelect }
+				title={ __( 'Move block position' ) }
+				leftAlign={ true }
+				hideCancelButton={ Platform.OS !== 'ios' }
+			/>
 		</>
 	);
 };
@@ -83,6 +145,7 @@ export default compose(
 
 		return {
 			firstIndex,
+			numberOfBlocks: blockOrder.length - 1,
 			isFirst: firstIndex === 0,
 			isLast: lastIndex === blockOrder.length - 1,
 			isLocked: getTemplateLock( rootClientId ) === 'all',
@@ -90,12 +153,19 @@ export default compose(
 		};
 	} ),
 	withDispatch( ( dispatch, { clientIds, rootClientId } ) => {
-		const { moveBlocksDown, moveBlocksUp } = dispatch(
+		const { moveBlocksDown, moveBlocksUp, moveBlocksToPosition } = dispatch(
 			'core/block-editor'
 		);
 		return {
 			onMoveDown: partial( moveBlocksDown, clientIds, rootClientId ),
 			onMoveUp: partial( moveBlocksUp, clientIds, rootClientId ),
+			onLongMove: ( targetIndex ) =>
+				partial(
+					moveBlocksToPosition,
+					clientIds,
+					rootClientId,
+					targetIndex
+				),
 		};
 	} ),
 	withInstanceId
diff --git a/packages/block-editor/src/components/block-mover/test/__snapshots__/index.native.js.snap b/packages/block-editor/src/components/block-mover/test/__snapshots__/index.native.js.snap
new file mode 100644
index 00000000000000..65269234f413f3
--- /dev/null
+++ b/packages/block-editor/src/components/block-mover/test/__snapshots__/index.native.js.snap
@@ -0,0 +1,51 @@
+// Jest Snapshot v1, https://goo.gl/fbAQLP
+
+exports[`Block Mover Picker should match snapshot 1`] = `
+<Fragment>
+  <ForwardRef(ToolbarButton)
+    extraProps={
+      Object {
+        "hint": "Double tap to move the block up",
+      }
+    }
+    icon={
+      <SVG
+        viewBox="-2 -2 24 24"
+        xmlns="http://www.w3.org/2000/svg"
+      >
+        <Path
+          d="M11 18H9V6l-4 4-2-1 7-7 7 7-2 1-4-4v12z"
+        />
+      </SVG>
+    }
+    onLongPress={[Function]}
+    title="Move block up from row NaN to row NaN"
+  />
+  <ForwardRef(ToolbarButton)
+    extraProps={
+      Object {
+        "hint": "Double tap to move the block down",
+      }
+    }
+    icon={
+      <SVG
+        viewBox="-2 -2 24 24"
+        xmlns="http://www.w3.org/2000/svg"
+      >
+        <Path
+          d="M9 2h2v12l4-4 2 1-7 7-7-7 2-1 4 4V2z"
+        />
+      </SVG>
+    }
+    onLongPress={[Function]}
+    title="Move block down from row NaN to row NaN"
+  />
+  <Picker
+    hideCancelButton={true}
+    leftAlign={true}
+    onChange={[Function]}
+    options={Array []}
+    title="Move block position"
+  />
+</Fragment>
+`;
diff --git a/packages/block-editor/src/components/block-mover/test/index.native.js b/packages/block-editor/src/components/block-mover/test/index.native.js
new file mode 100644
index 00000000000000..113d61e84cf254
--- /dev/null
+++ b/packages/block-editor/src/components/block-mover/test/index.native.js
@@ -0,0 +1,51 @@
+/**
+ * External dependencies
+ */
+import { shallow } from 'enzyme';
+
+/**
+ * Internal dependencies
+ */
+import { BlockMover } from '../index';
+
+describe( 'Block Mover Picker', () => {
+	it( 'renders without crashing', () => {
+		const wrapper = shallow( <BlockMover />, {
+			context: {
+				isFirst: false,
+				isLast: true,
+				isLocked: false,
+				numberOfBlocks: 2,
+				firstIndex: 1,
+
+				onMoveDown: jest.fn(),
+				onMoveUp: jest.fn(),
+				onLongPress: jest.fn(),
+
+				rootClientId: '',
+				isStackedHorizontally: true,
+			},
+		} );
+		expect( wrapper ).toBeTruthy();
+	} );
+
+	it( 'should match snapshot', () => {
+		const wrapper = shallow( <BlockMover />, {
+			context: {
+				isFirst: false,
+				isLast: true,
+				isLocked: false,
+				numberOfBlocks: 2,
+				firstIndex: 1,
+
+				onMoveDown: jest.fn(),
+				onMoveUp: jest.fn(),
+				onLongPress: jest.fn(),
+
+				rootClientId: '',
+				isStackedHorizontally: true,
+			},
+		} );
+		expect( wrapper ).toMatchSnapshot();
+	} );
+} );