Index: src/wp-admin/edit-form-advanced.php
===================================================================
--- src/wp-admin/edit-form-advanced.php	(revision 39362)
+++ src/wp-admin/edit-form-advanced.php	(working copy)
@@ -246,17 +246,19 @@
 // all taxonomies
 foreach ( get_object_taxonomies( $post ) as $tax_name ) {
 	$taxonomy = get_taxonomy( $tax_name );
-	if ( ! $taxonomy->show_ui || false === $taxonomy->meta_box_cb )
+	if ( ! $taxonomy->show_ui || false === $taxonomy->meta_box_cb ) {
 		continue;
+	}
 
 	$label = $taxonomy->labels->name;
 
-	if ( ! is_taxonomy_hierarchical( $tax_name ) )
+	if ( ! is_taxonomy_hierarchical( $tax_name ) ) {
 		$tax_meta_box_id = 'tagsdiv-' . $tax_name;
-	else
+	} else {
 		$tax_meta_box_id = $tax_name . 'div';
+	}
 
-	add_meta_box( $tax_meta_box_id, $label, $taxonomy->meta_box_cb, null, 'side', 'core', array( 'taxonomy' => $tax_name ) );
+	add_meta_box( $tax_meta_box_id, $label, $taxonomy->meta_box_cb, null, $taxonomy->meta_box_context , $taxonomy->meta_box_priority, array( 'taxonomy' => $tax_name ) );
 }
 
 if ( post_type_supports( $post_type, 'page-attributes' ) || count( get_page_templates( $post ) ) > 0 ) {
Index: src/wp-includes/class-wp-taxonomy.php
===================================================================
--- src/wp-includes/class-wp-taxonomy.php	(revision 39362)
+++ src/wp-includes/class-wp-taxonomy.php	(working copy)
@@ -142,6 +142,24 @@
 	public $meta_box_cb = null;
 
 	/**
+	 * The context for the meta box display.
+	 *
+	 * @since 4.8.0
+	 * @access public
+	 * @var string
+	 */
+	public $meta_box_context = 'side';
+
+	/**
+	 * The priority for the meta box display.
+	 *
+	 * @since 4.8.0
+	 * @access public
+	 * @var string
+	 */
+	public $meta_box_priority = 'core';
+
+	/**
 	 * An array of object types this taxonomy is registered for.
 	 *
 	 * @since 4.7.0
@@ -250,6 +268,8 @@
 			'show_in_quick_edit'    => null,
 			'show_admin_column'     => false,
 			'meta_box_cb'           => null,
+			'meta_box_context'      => 'side',
+			'meta_box_priority'     => 'core',
 			'capabilities'          => array(),
 			'rewrite'               => true,
 			'query_var'             => $this->name,
Index: src/wp-includes/taxonomy.php
===================================================================
--- src/wp-includes/taxonomy.php	(revision 39362)
+++ src/wp-includes/taxonomy.php	(working copy)
@@ -294,6 +294,7 @@
  * @since 4.4.0 The `show_ui` argument is now enforced on the term editing screen.
  * @since 4.4.0 The `public` argument now controls whether the taxonomy can be queried on the front end.
  * @since 4.5.0 Introduced `publicly_queryable` argument.
+ * @since 4.8.0 Introduced `meta_box_context` and `meta_box_priority` argument.
  *
  * @global array $wp_taxonomies Registered taxonomies.
  *
@@ -333,6 +334,10 @@
  *                                                post_categories_meta_box() is used for hierarchical taxonomies, and
  *                                                post_tags_meta_box() is used for non-hierarchical. If false, no meta
  *                                                box is shown.
+ *     @type string        $meta_box_context      The context within the screen where the meta box is displayed.
+ *                                                Accepts 'side', 'normal' and 'advanced'. Default value: 'side'.
+ *     @type string        $meta_box_priority     The priority within the context where the meta box is displayed.
+ *                                                Accepts 'high', 'core', 'default' and 'low'. Default value: 'core'.
  *     @type array         $capabilities {
  *         Array of capabilities for this taxonomy.
  *