diff --git a/wp-includes/class-wp-theme-json.php b/wp-includes/class-wp-theme-json.php
index 227ae7c224..a35ee1b795 100644
--- a/wp-includes/class-wp-theme-json.php
+++ b/wp-includes/class-wp-theme-json.php
@@ -179,6 +179,9 @@ class WP_Theme_JSON {
 	 * @var array
 	 */
 	const ALLOWED_SETTINGS = array(
+		'border'     => array(
+			'customRadius' => null,
+		),
 		'color'      => array(
 			'custom'         => null,
 			'customDuotone'  => null,
@@ -211,6 +214,9 @@ class WP_Theme_JSON {
 	 * @var array
 	 */
 	const ALLOWED_STYLES = array(
+		'border'     => array(
+			'radius' => null,
+		),
 		'color'      => array(
 			'background' => null,
 			'gradient'   => null,
diff --git a/wp-includes/theme.json b/wp-includes/theme.json
index 21dae95faf..17389579ea 100644
--- a/wp-includes/theme.json
+++ b/wp-includes/theme.json
@@ -1,6 +1,9 @@
 {
 	"version": 1,
 	"settings": {
+		"border": {
+			"customRadius": false
+		},
 		"color": {
 			"custom": true,
 			"customDuotone": true,
@@ -209,6 +212,13 @@
 					"size": "42px"
 				}
 			]
+		},
+		"blocks": {
+			"core/button": {
+				"border": {
+					"customRadius": true
+				}
+			}
 		}
 	}
 }
diff --git a/wp-includes/version.php b/wp-includes/version.php
index d5f9cff5fa..407f0fa590 100644
--- a/wp-includes/version.php
+++ b/wp-includes/version.php
@@ -13,7 +13,7 @@
  *
  * @global string $wp_version
  */
-$wp_version = '5.9-alpha-51537';
+$wp_version = '5.9-alpha-51538';
 
 /**
  * Holds the WordPress DB revision, increments when changes are made to the WordPress DB schema.