diff --git a/packages/block-library/src/search/block.json b/packages/block-library/src/search/block.json
index d57ba7fd9c3900..7d94a640f7ef73 100644
--- a/packages/block-library/src/search/block.json
+++ b/packages/block-library/src/search/block.json
@@ -34,6 +34,9 @@
 	},
 	"supports": {
 		"align": [ "left", "center", "right" ],
-		"html": false
+		"html": false,
+		"__experimentalBorder": {
+			"radius": true
+		}
 	}
 }
diff --git a/packages/block-library/src/search/edit.js b/packages/block-library/src/search/edit.js
index c82086f2e5ff33..ebb566c18583f0 100644
--- a/packages/block-library/src/search/edit.js
+++ b/packages/block-library/src/search/edit.js
@@ -53,6 +53,12 @@ const CSS_UNITS = [
 	{ value: 'px', label: 'px', default: PX_WIDTH_DEFAULT },
 ];
 
+// Used to calculate adjustment to inner button border radius.
+const DEFAULT_INPUT_PADDING = 4;
+
+// Minimum inner radius of 1px as having none when there is an outer radius jars.
+const MIN_INNER_RADIUS = 1;
+
 export default function SearchEdit( {
 	className,
 	attributes,
@@ -70,8 +76,10 @@ export default function SearchEdit( {
 		buttonText,
 		buttonPosition,
 		buttonUseIcon,
+		style,
 	} = attributes;
 
+	const borderRadius = style?.border?.radius;
 	const unitControlInstanceId = useInstanceId( UnitControl );
 	const unitControlInputId = `wp-block-search__width-${ unitControlInstanceId }`;
 
@@ -123,10 +131,33 @@ export default function SearchEdit( {
 		};
 	};
 
+	const getInnerBorderRadiusStyle = () => {
+		if ( ! borderRadius ) {
+			return undefined;
+		}
+
+		if ( 'button-inside' === buttonPosition ) {
+			const radius = Math.max(
+				borderRadius - DEFAULT_INPUT_PADDING,
+				MIN_INNER_RADIUS
+			);
+			return radius ? `${ radius }px` : undefined;
+		}
+
+		return `${ borderRadius }px`;
+	};
+
+	const sharedStyles = {
+		borderRadius: getInnerBorderRadiusStyle(),
+	};
+
 	const renderTextField = () => {
+		const textFieldStyles = { ...sharedStyles };
+
 		return (
 			<input
 				className="wp-block-search__input"
+				style={ textFieldStyles }
 				aria-label={ __( 'Optional placeholder text' ) }
 				// We hide the placeholder field's placeholder when there is a value. This
 				// stops screen readers from reading the placeholder field's placeholder
@@ -143,18 +174,22 @@ export default function SearchEdit( {
 	};
 
 	const renderButton = () => {
+		const buttonStyles = { ...sharedStyles };
+
 		return (
 			<>
 				{ buttonUseIcon && (
 					<Button
 						icon={ search }
 						className="wp-block-search__button"
+						style={ buttonStyles }
 					/>
 				) }
 
 				{ ! buttonUseIcon && (
 					<RichText
 						className="wp-block-search__button"
+						style={ buttonStyles }
 						aria-label={ __( 'Button text' ) }
 						placeholder={ __( 'Add button text…' ) }
 						withoutInteractiveFormatting
@@ -168,6 +203,52 @@ export default function SearchEdit( {
 		);
 	};
 
+	const renderInputs = () => {
+		const wrapperStyles =
+			'button-inside' === buttonPosition
+				? {
+						borderRadius: borderRadius
+							? `${ borderRadius }px`
+							: undefined,
+				  }
+				: {};
+
+		return (
+			<ResizableBox
+				size={ { width: `${ width }${ widthUnit }` } }
+				className="wp-block-search__inside-wrapper"
+				style={ wrapperStyles }
+				minWidth={ MIN_WIDTH }
+				enable={ getResizableSides() }
+				onResizeStart={ ( event, direction, elt ) => {
+					setAttributes( {
+						width: parseInt( elt.offsetWidth, 10 ),
+						widthUnit: 'px',
+					} );
+					toggleSelection( false );
+				} }
+				onResizeStop={ ( event, direction, elt, delta ) => {
+					setAttributes( {
+						width: parseInt( width + delta.width, 10 ),
+					} );
+					toggleSelection( true );
+				} }
+				showHandle={ isSelected }
+			>
+				{ ( 'button-inside' === buttonPosition ||
+					'button-outside' === buttonPosition ) && (
+					<>
+						{ renderTextField() }
+						{ renderButton() }
+					</>
+				) }
+
+				{ 'button-only' === buttonPosition && renderButton() }
+				{ 'no-button' === buttonPosition && renderTextField() }
+			</ResizableBox>
+		);
+	};
+
 	const controls = (
 		<>
 			<BlockControls>
@@ -243,7 +324,7 @@ export default function SearchEdit( {
 			</BlockControls>
 
 			<InspectorControls>
-				<PanelBody title={ __( 'Display Settings' ) }>
+				<PanelBody title={ __( 'Display settings' ) }>
 					<BaseControl
 						label={ __( 'Width' ) }
 						id={ unitControlInputId }
@@ -327,39 +408,7 @@ export default function SearchEdit( {
 				/>
 			) }
 
-			<ResizableBox
-				size={ {
-					width: `${ width }${ widthUnit }`,
-				} }
-				className="wp-block-search__inside-wrapper"
-				minWidth={ MIN_WIDTH }
-				enable={ getResizableSides() }
-				onResizeStart={ ( event, direction, elt ) => {
-					setAttributes( {
-						width: parseInt( elt.offsetWidth, 10 ),
-						widthUnit: 'px',
-					} );
-					toggleSelection( false );
-				} }
-				onResizeStop={ ( event, direction, elt, delta ) => {
-					setAttributes( {
-						width: parseInt( width + delta.width, 10 ),
-					} );
-					toggleSelection( true );
-				} }
-				showHandle={ isSelected }
-			>
-				{ ( 'button-inside' === buttonPosition ||
-					'button-outside' === buttonPosition ) && (
-					<>
-						{ renderTextField() }
-						{ renderButton() }
-					</>
-				) }
-
-				{ 'button-only' === buttonPosition && renderButton() }
-				{ 'no-button' === buttonPosition && renderTextField() }
-			</ResizableBox>
+			{ renderInputs() }
 		</div>
 	);
 }
diff --git a/packages/block-library/src/search/index.php b/packages/block-library/src/search/index.php
index 36607188ff44a3..5c2bdd5e1bcc18 100644
--- a/packages/block-library/src/search/index.php
+++ b/packages/block-library/src/search/index.php
@@ -36,7 +36,8 @@ function render_block_core_search( $attributes ) {
 	$label_markup    = '';
 	$input_markup    = '';
 	$button_markup   = '';
-	$width_styles    = '';
+
+	$border_radius_css = block_core_search_build_css_border_radius( $attributes );
 
 	if ( $show_label ) {
 		if ( ! empty( $attributes['label'] ) ) {
@@ -55,9 +56,14 @@ function render_block_core_search( $attributes ) {
 	}
 
 	if ( $show_input ) {
+		$input_styles = ! empty( $border_radius_css['style'] )
+			? sprintf( ' style="%s"', esc_attr( $border_radius_css['style'] ) )
+			: '';
+
 		$input_markup = sprintf(
-			'<input type="search" id="%s" class="wp-block-search__input" name="s" value="%s" placeholder="%s" required />',
+			'<input type="search" id="%s" class="wp-block-search__input"%s name="s" value="%s" placeholder="%s" required />',
 			$input_id,
+			$input_styles,
 			esc_attr( get_search_query() ),
 			esc_attr( $attributes['placeholder'] )
 		);
@@ -66,6 +72,9 @@ function render_block_core_search( $attributes ) {
 	if ( $show_button ) {
 		$button_internal_markup = '';
 		$button_classes         = '';
+		$button_styles          = ! empty( $border_radius_css['style'] )
+			? sprintf( ' style="%s"', esc_attr( $border_radius_css['style'] ) )
+			: '';
 
 		if ( ! $use_icon_button ) {
 			if ( ! empty( $attributes['buttonText'] ) ) {
@@ -80,22 +89,29 @@ function render_block_core_search( $attributes ) {
 		}
 
 		$button_markup = sprintf(
-			'<button type="submit"class="wp-block-search__button ' . $button_classes . '">%s</button>',
+			'<button type="submit" class="wp-block-search__button %s"%s>%s</button>',
+			$button_classes,
+			$button_styles,
 			$button_internal_markup
 		);
 	}
 
+	$field_styles = ( array_key_exists( 'buttonPosition', $attributes ) && 'button-inside' === $attributes['buttonPosition'] )
+		? $border_radius_css['wrapper_style']
+		: '';
+
 	if ( ! empty( $attributes['width'] ) && ! empty( $attributes['widthUnit'] ) ) {
 		if ( ! empty( $attributes['buttonPosition'] ) && 'button-only' !== $attributes['buttonPosition'] ) {
-			$width_styles = ' style="width: ' . $attributes['width'] . $attributes['widthUnit'] . ';"';
+			$field_styles .= ' width: ' . $attributes['width'] . $attributes['widthUnit'] . ';"';
 		}
 	}
 
-	$field_markup       = sprintf(
+	$field_markup = sprintf(
 		'<div class="wp-block-search__inside-wrapper"%s>%s</div>',
-		$width_styles,
+		( ! empty( $field_styles ) ) ? sprintf( ' style="%s"', esc_attr( $field_styles ) ) : '',
 		$input_markup . $button_markup
 	);
+
 	$wrapper_attributes = get_block_wrapper_attributes( array( 'class' => $classnames ) );
 
 	return sprintf(
@@ -119,6 +135,39 @@ function register_block_core_search() {
 }
 add_action( 'init', 'register_block_core_search' );
 
+/**
+ * Build an array with inline styles defining the border radius
+ * which will be applied to the inner elements and wrapper of the search block
+ * on the frontend.
+ *
+ * @param  array $attributes Search block attributes.
+ * @return array Border radius inline styles.
+ */
+function block_core_search_build_css_border_radius( $attributes ) {
+	$padding       = 4;
+	$border_radius = array(
+		'style'         => '',
+		'wrapper_style' => '',
+	);
+
+	$has_border_radius = isset( $attributes['style']['border']['radius'] );
+	if ( ! $has_border_radius ) {
+		return $border_radius;
+	}
+
+	$radius_value  = $attributes['style']['border']['radius'];
+	$button_inside = array_key_exists( 'buttonPosition', $attributes )
+		&& 'button-inside' === $attributes['buttonPosition'];
+
+	// Uses min value of 1 as having no radius when the outer does is jarring.
+	$radius = $button_inside ? max( $radius_value - $padding, 1 ) : $radius_value;
+
+	$border_radius['style']         = sprintf( 'border-radius: %spx;', esc_attr( $radius ) );
+	$border_radius['wrapper_style'] = sprintf( 'border-radius: %spx;', esc_attr( $radius_value ) );
+
+	return $border_radius;
+}
+
 /**
  * Builds the correct top level classnames for the 'core/search' block.
  *