diff --git a/packages/block-library/src/cover/block.json b/packages/block-library/src/cover/block.json
index 852b9ab30d1c9..e763cd9f047d9 100644
--- a/packages/block-library/src/cover/block.json
+++ b/packages/block-library/src/cover/block.json
@@ -86,6 +86,18 @@
 			"__experimentalDuotone": "> .wp-block-cover__image-background, > .wp-block-cover__video-background",
 			"text": false,
 			"background": false
+		},
+		"__experimentalBorder": {
+			"color": true,
+			"radius": true,
+			"style": true,
+			"width": true,
+			"__experimentalDefaultControls": {
+				"color": false,
+				"radius": false,
+				"style": false,
+				"width": false
+			}
 		}
 	},
 	"editorStyle": "wp-block-cover-editor",
diff --git a/packages/block-library/src/cover/style.scss b/packages/block-library/src/cover/style.scss
index db543cb731e5c..1088aef381ad8 100644
--- a/packages/block-library/src/cover/style.scss
+++ b/packages/block-library/src/cover/style.scss
@@ -12,6 +12,12 @@
 	// This block has customizable padding, border-box makes that more predictable.
 	box-sizing: border-box;
 
+	> span,
+	> img,
+	> video {
+		border-radius: inherit;
+	}
+
 	&.has-parallax {
 		background-attachment: fixed;
 
@@ -72,6 +78,7 @@
 		right: 0;
 		z-index: z-index(".wp-block-cover.has-background-dim::before");
 		opacity: 0.5;
+		border-radius: inherit;
 	}
 
 	// The following styles are needed to support legacy blocks added prior to the update
diff --git a/packages/block-library/src/post-featured-image/block.json b/packages/block-library/src/post-featured-image/block.json
index 982ba9ac68e8b..ecddc24aa9c39 100644
--- a/packages/block-library/src/post-featured-image/block.json
+++ b/packages/block-library/src/post-featured-image/block.json
@@ -37,6 +37,18 @@
 		"spacing": {
 			"margin": true,
 			"padding": true
+		},
+		"__experimentalBorder": {
+			"color": true,
+			"radius": true,
+			"style": true,
+			"width": true,
+			"__experimentalDefaultControls": {
+				"color": false,
+				"radius": false,
+				"style": false,
+				"width": false
+			}
 		}
 	},
 	"editorStyle": "wp-block-post-featured-image-editor",
diff --git a/packages/block-library/src/post-featured-image/editor.scss b/packages/block-library/src/post-featured-image/editor.scss
index 31a77623c335c..da5b4757f9269 100644
--- a/packages/block-library/src/post-featured-image/editor.scss
+++ b/packages/block-library/src/post-featured-image/editor.scss
@@ -15,6 +15,7 @@
 		align-items: center;
 		box-shadow: none;
 		padding: 0;
+		border-radius: inherit;
 
 		// Hide the upload button, as it's also available in the media library.
 		.components-form-file-upload {
diff --git a/packages/block-library/src/post-featured-image/style.scss b/packages/block-library/src/post-featured-image/style.scss
index 85ca80b427e61..d76e93659f9e9 100644
--- a/packages/block-library/src/post-featured-image/style.scss
+++ b/packages/block-library/src/post-featured-image/style.scss
@@ -11,6 +11,13 @@
 		vertical-align: bottom;
 	}
 
+	&:not(.is-style-rounded) {
+		> a,
+		img {
+			border-radius: inherit;
+		}
+	}
+
 	&.alignwide img,
 	&.alignfull img {
 		width: 100%;