diff --git a/src/wp-includes/taxonomy.php b/src/wp-includes/taxonomy.php
index 94f36689fd..f1c1bce307 100644
--- a/src/wp-includes/taxonomy.php
+++ b/src/wp-includes/taxonomy.php
@@ -1841,10 +1841,30 @@ function wp_get_object_terms($object_ids, $taxonomies, $args = array()) {
 
 	$args = wp_parse_args( $args );
 
+	/*
+	 * When one or more queried taxonomies is registered with an 'args' array,
+	 * those params override the `$args` passed to this function.
+	 */
+	$terms = array();
+	if ( count( $taxonomies ) > 1 ) {
+		foreach ( $taxonomies as $index => $taxonomy ) {
+			$t = get_taxonomy( $taxonomy );
+			if ( isset( $t->args ) && is_array( $t->args ) && $args != array_merge( $args, $t->args ) ) {
+				unset( $taxonomies[ $index ] );
+				$terms = array_merge( $terms, wp_get_object_terms( $object_ids, $taxonomy, array_merge( $args, $t->args ) ) );
+			}
+		}
+	} else {
+		$t = get_taxonomy( $taxonomies[0] );
+		if ( isset( $t->args ) && is_array( $t->args ) ) {
+			$args = array_merge( $args, $t->args );
+		}
+	}
+
 	$args['taxonomy'] = $taxonomies;
 	$args['object_ids'] = $object_ids;
 
-	$terms = get_terms( $args );
+	$terms = array_merge( $terms, get_terms( $args ) );
 
 	/**
 	 * Filters the terms for a given object or objects.
diff --git a/tests/phpunit/tests/term/query.php b/tests/phpunit/tests/term/query.php
index 4a15f1e53f..b2e2a27621 100644
--- a/tests/phpunit/tests/term/query.php
+++ b/tests/phpunit/tests/term/query.php
@@ -381,4 +381,50 @@ class Tests_Term_Query extends WP_UnitTestCase {
 		$count = $query->get_terms();
 		$this->assertEquals( 1, $count );
 	}
+
+	/**
+	 * @ticket 40496
+	 */
+	public function test_get_the_terms_should_respect_taxonomy_orderby() {
+		register_taxonomy( 'wptests_tax', 'post', array(
+			'sort' => true,
+			'args' => array(
+				'orderby' => 'term_order',
+			),
+		) );
+		$term_ids = self::factory()->term->create_many( 2, array(
+			'taxonomy' => 'wptests_tax',
+		) );
+		$post_id = self::factory()->post->create();
+		wp_set_object_terms( $post_id, array( $term_ids[0], $term_ids[1] ), 'wptests_tax' );
+		$terms = get_the_terms( $post_id, 'wptests_tax' );
+		$this->assertEquals( array( $term_ids[0], $term_ids[1] ), wp_list_pluck( $terms, 'term_id' ) );
+		// Flip the order
+		wp_set_object_terms( $post_id, array( $term_ids[1], $term_ids[0] ), 'wptests_tax' );
+		$terms = get_the_terms( $post_id, 'wptests_tax' );
+		$this->assertEquals( array( $term_ids[1], $term_ids[0] ), wp_list_pluck( $terms, 'term_id' ) );
+	}
+
+	/**
+	 * @ticket 40496
+	 */
+	public function test_wp_get_object_terms_should_respect_taxonomy_orderby() {
+		register_taxonomy( 'wptests_tax', 'post', array(
+			'sort' => true,
+			'args' => array(
+				'orderby' => 'term_order',
+			),
+		) );
+		$term_ids = self::factory()->term->create_many( 2, array(
+			'taxonomy' => 'wptests_tax',
+		) );
+		$post_id = self::factory()->post->create();
+		wp_set_object_terms( $post_id, array( $term_ids[0], $term_ids[1] ), 'wptests_tax' );
+		$terms = wp_get_object_terms( $post_id, array( 'category', 'wptests_tax' ) );
+		$this->assertEquals( array( $term_ids[0], $term_ids[1], 1 ), wp_list_pluck( $terms, 'term_id' ) );
+		// Flip the order
+		wp_set_object_terms( $post_id, array( $term_ids[1], $term_ids[0] ), 'wptests_tax' );
+		$terms = wp_get_object_terms( $post_id, array( 'category', 'wptests_tax' ) );
+		$this->assertEquals( array( $term_ids[1], $term_ids[0], 1 ), wp_list_pluck( $terms, 'term_id' ) );
+	}
 }