diff --git a/editor/block-mover/generate-order-title.js b/editor/block-mover/generate-order-title.js
new file mode 100644
index 00000000000000..646558f576aa0c
--- /dev/null
+++ b/editor/block-mover/generate-order-title.js
@@ -0,0 +1,29 @@
+export default function( { typeTitle, position, isFirst, isLast, dir } ) {
+	if ( isFirst && isLast ) {
+		return `Block "${ typeTitle }" is the only block, and cannot be moved`;
+	}
+
+	if ( dir > 0 && ! isLast ) {
+		// moving down
+		return `Move "${ typeTitle }" block from position ${ position }` +
+			` down to position ${ position + 1 }`;
+	}
+
+	if ( dir > 0 && isLast ) {
+		// moving down, and is the last item
+		return `Block "${ typeTitle }" is at the end of the content and can’t be moved down`;
+	}
+
+	if ( dir < 0 && ! isFirst ) {
+		// moving up
+		return `Move "${ typeTitle }" block from position ${ position }` +
+			` up to position ${ position - 1 }`;
+	}
+
+	if ( dir < 0 && isFirst ) {
+		// moving up, and is the first item
+		return `Block "${ typeTitle }" is at the beginning of the content and can’t be moved up`;
+	}
+
+	return '';
+}
diff --git a/editor/block-mover/index.js b/editor/block-mover/index.js
index f040d2394a67f2..53cce706e4c42e 100644
--- a/editor/block-mover/index.js
+++ b/editor/block-mover/index.js
@@ -13,25 +13,32 @@ import { IconButton } from 'components';
  * Internal dependencies
  */
 import './style.scss';
-import { isFirstBlock, isLastBlock } from '../selectors';
+import { isFirstBlock, isLastBlock, getBlock } from '../selectors';
+import { getBlockSettings } from '../../blocks/api/registration';
+import generateOrderTitle from './generate-order-title';
 
-function BlockMover( { onMoveUp, onMoveDown, isFirst, isLast } ) {
+function BlockMover( { onMoveUp, onMoveDown, isFirst, isLast, block, order } ) {
 	// We emulate a disabled state because forcefully applying the `disabled`
 	// attribute on the button while it has focus causes the screen to change
 	// to an unfocused state (body as active element) without firing blur on,
 	// the rendering parent, leaving it unable to react to focus out.
+	const type = getBlockSettings( block.blockType ),
+		typeTitle = type.title,
+		position = ( order + 1 );
 
 	return (
 		<div className="editor-block-mover">
 			<IconButton
 				className="editor-block-mover__control"
 				onClick={ isFirst ? null : onMoveUp }
+				label={ generateOrderTitle( { typeTitle, position, isFirst, isLast, dir: -1 } ) }
 				icon="arrow-up-alt2"
 				aria-disabled={ isFirst }
 			/>
 			<IconButton
 				className="editor-block-mover__control"
 				onClick={ isLast ? null : onMoveDown }
+				label={ generateOrderTitle( { typeTitle, position, isFirst, isLast, dir: 1 } ) }
 				icon="arrow-down-alt2"
 				aria-disabled={ isLast }
 			/>
@@ -43,6 +50,7 @@ export default connect(
 	( state, ownProps ) => ( {
 		isFirst: isFirstBlock( state, first( ownProps.uids ) ),
 		isLast: isLastBlock( state, last( ownProps.uids ) ),
+		block: getBlock( state, ownProps.uid ),
 	} ),
 	( dispatch, ownProps ) => ( {
 		onMoveDown() {
diff --git a/editor/block-mover/style.scss b/editor/block-mover/style.scss
index a7b69706e7009f..f184f10a818696 100644
--- a/editor/block-mover/style.scss
+++ b/editor/block-mover/style.scss
@@ -10,13 +10,13 @@
 	border: none;
 	outline: none;
 	background: none;
-	color: $dark-gray-100;
+	color: $dark-gray-300;
 	cursor: pointer;
 	width: 20px;
 	height: 20px;
 
 	&:hover {
-		color: $dark-gray-900;
+		color: $dark-gray-500;
 	}
 
 	&[aria-disabled="true"] {
diff --git a/editor/block-mover/test/generate-order-title.js b/editor/block-mover/test/generate-order-title.js
new file mode 100644
index 00000000000000..fb7c18eb0e52e7
--- /dev/null
+++ b/editor/block-mover/test/generate-order-title.js
@@ -0,0 +1,75 @@
+/**
+ * External dependencies
+ */
+import { expect } from 'chai';
+
+/**
+ * Internal dependencies
+ */
+import generateOrderTitle from '../generate-order-title';
+
+describe( 'block mover', () => {
+	describe( 'generateOrderTitle', () => {
+		const typeTitle = 'TestType';
+
+		it( 'Should generate a title for the first item moving up', () => {
+			expect( generateOrderTitle( {
+				typeTitle,
+				position: 1,
+				isFirst: true,
+				isLast: false,
+				dir: -1,
+			} ) ).to.equal(
+				'Block "' + typeTitle + '" is at the beginning of the content and can’t be moved up'
+			);
+		} );
+
+		it( 'Should generate a title for the last item moving down', () => {
+			expect( generateOrderTitle( {
+				typeTitle,
+				position: 1,
+				isFirst: false,
+				isLast: true,
+				dir: 1,
+			} ) ).to.equal(
+				'Block "' + typeTitle + '" is at the end of the content and can’t be moved down'
+			);
+		} );
+
+		it( 'Should generate a title for the second item moving up', () => {
+			expect( generateOrderTitle( {
+				typeTitle,
+				position: 2,
+				isFirst: false,
+				isLast: false,
+				dir: -1,
+			} ) ).to.equal(
+				'Move "' + typeTitle + '" block from position 2 up to position 1'
+			);
+		} );
+
+		it( 'Should generate a title for the second item moving down', () => {
+			expect( generateOrderTitle( {
+				typeTitle,
+				position: 2,
+				isFirst: false,
+				isLast: false,
+				dir: 1,
+			} ) ).to.equal(
+				'Move "' + typeTitle + '" block from position 2 down to position 3'
+			);
+		} );
+
+		it( 'Should generate a title for the only item in the list', () => {
+			expect( generateOrderTitle( {
+				typeTitle,
+				position: 1,
+				isFirst: true,
+				isLast: true,
+				dir: 1,
+			} ) ).to.equal(
+				'Block "' + typeTitle + '" is the only block, and cannot be moved'
+			);
+		} );
+	} );
+} );
diff --git a/editor/modes/visual-editor/block.js b/editor/modes/visual-editor/block.js
index cc93ddf663d919..d883b6c52c10b6 100644
--- a/editor/modes/visual-editor/block.js
+++ b/editor/modes/visual-editor/block.js
@@ -232,7 +232,7 @@ class VisualEditorBlock extends wp.element.Component {
 				tabIndex="0"
 				{ ...wrapperProps }
 			>
-				{ ( showUI || isHovered ) && <BlockMover uids={ [ block.uid ] } /> }
+				{ ( showUI || isHovered ) && <BlockMover uid={ block.uid } order={ this.props.order } /> }
 				{ showUI &&
 					<CSSTransitionGroup
 						transitionName={ { appear: 'is-appearing', appearActive: 'is-appearing-active' } }