diff --git a/packages/block-library/src/post-terms/index.js b/packages/block-library/src/post-terms/index.js
index 6749a1197c83c..37f1a403eddd2 100644
--- a/packages/block-library/src/post-terms/index.js
+++ b/packages/block-library/src/post-terms/index.js
@@ -3,18 +3,16 @@
  */
 import metadata from './block.json';
 import edit from './edit';
-import variations from './variations';
 
 /**
  * WordPress dependencies
  */
-import { postTerms as icon } from '@wordpress/icons';
+import { postCategories as icon } from '@wordpress/icons';
 
 const { name } = metadata;
 export { metadata, name };
 
 export const settings = {
 	icon,
-	variations,
 	edit,
 };
diff --git a/packages/block-library/src/post-terms/index.php b/packages/block-library/src/post-terms/index.php
index d1902b93a82f9..97cc1ebc0ffdb 100644
--- a/packages/block-library/src/post-terms/index.php
+++ b/packages/block-library/src/post-terms/index.php
@@ -49,10 +49,49 @@ function render_block_core_post_terms( $attributes, $content, $block ) {
  * Registers the `core/post-terms` block on the server.
  */
 function register_block_core_post_terms() {
+	$taxonomies = get_taxonomies(
+		array(
+			'public'       => true,
+			'show_in_rest' => true,
+		),
+		'objects'
+	);
+
+	// Split the available taxonomies to `built_in` and custom ones,
+	// in order to prioritize the `built_in` taxonomies at the
+	// search results.
+	$built_ins         = array();
+	$custom_variations = array();
+
+	// Create and register the eligible taxonomies variations.
+	foreach ( $taxonomies as $taxonomy ) {
+		$variation = array(
+			'name'        => $taxonomy->name,
+			/* translators: %s: taxonomy's label */
+			'title'       => sprintf( __( 'Post %s' ), $taxonomy->label ),
+			/* translators: %s: taxonomy's label */
+			'description' => sprintf( __( "Display a post's %s" ), $taxonomy->label ),
+			'attributes'  => array(
+				'term' => $taxonomy->name,
+			),
+			'isActive'    => array( 'term' ),
+		);
+		// Set the category variation as the default one.
+		if ( 'category' === $taxonomy->name ) {
+			$variation['isDefault'] = true;
+		}
+		if ( $taxonomy->_builtin ) {
+			$built_ins[] = $variation;
+		} else {
+			$custom_variations[] = $variation;
+		}
+	}
+
 	register_block_type_from_metadata(
 		__DIR__ . '/post-terms',
 		array(
 			'render_callback' => 'render_block_core_post_terms',
+			'variations'      => array_merge( $built_ins, $custom_variations ),
 		)
 	);
 }
diff --git a/packages/block-library/src/post-terms/variations.js b/packages/block-library/src/post-terms/variations.js
deleted file mode 100644
index 14ddb3cb09514..0000000000000
--- a/packages/block-library/src/post-terms/variations.js
+++ /dev/null
@@ -1,28 +0,0 @@
-/**
- * WordPress dependencies
- */
-import { __ } from '@wordpress/i18n';
-import { postCategories, postTerms } from '@wordpress/icons';
-
-const variations = [
-	{
-		name: 'category',
-		title: __( 'Post Categories' ),
-		description: __( "Display a post's categories." ),
-		icon: postCategories,
-		isDefault: true,
-		attributes: { term: 'category' },
-		isActive: ( blockAttributes ) => blockAttributes.term === 'category',
-	},
-
-	{
-		name: 'post_tag',
-		title: __( 'Post Tags' ),
-		description: __( "Display a post's tags." ),
-		icon: postTerms,
-		attributes: { term: 'post_tag' },
-		isActive: ( blockAttributes ) => blockAttributes.term === 'post_tag',
-	},
-];
-
-export default variations;