diff --git a/src/wp-includes/functions.php b/src/wp-includes/functions.php
index b71a83761c..2417bcdf76 100644
--- a/src/wp-includes/functions.php
+++ b/src/wp-includes/functions.php
@@ -1169,6 +1169,7 @@ function add_query_arg( ...$args ) {
 	$ret = preg_replace( '#=(&|$)#', '$1', $ret );
 	$ret = $protocol . $base . $ret . $frag;
 	$ret = rtrim( $ret, '?' );
+	$ret = str_replace( '?#', '#', $ret );
 	return $ret;
 }
 
diff --git a/tests/phpunit/tests/functions.php b/tests/phpunit/tests/functions.php
index bcf8525216..96dee380ec 100644
--- a/tests/phpunit/tests/functions.php
+++ b/tests/phpunit/tests/functions.php
@@ -665,6 +665,62 @@ class Tests_Functions extends WP_UnitTestCase {
 		$this->assertSame( 'foo=bar&1=2', $url );
 	}
 
+	/**
+	 * Tests that add_query_arg removes the question mark when
+	 * a parameter is set to false.
+	 *
+	 * @dataProvider data_add_query_arg_removes_question_mark
+	 *
+	 * @ticket 44499
+	 * @group  add_query_arg
+	 *
+	 * @covers ::add_query_arg
+	 *
+	 * @param string $url      Url to test.
+	 * @param string $expected Expected URL.
+	 */
+	public function test_add_query_arg_removes_question_mark( $url, $expected, $key = 'param', $value = false ) {
+		$this->assertSame( $expected, add_query_arg( $key, $value, $url ) );
+	}
+
+	/**
+	 * Data provider.
+	 *
+	 * @return array
+	 */
+	public function data_add_query_arg_removes_question_mark() {
+		return array(
+			'anchor'                                     => array(
+				'url'      => 'http://example.org?#anchor',
+				'expected' => 'http://example.org#anchor',
+			),
+			'/ then anchor'                              => array(
+				'url'      => 'http://example.org/?#anchor',
+				'expected' => 'http://example.org/#anchor',
+			),
+			'invalid query param and anchor'             => array(
+				'url'      => 'http://example.org?param=value#anchor',
+				'expected' => 'http://example.org#anchor',
+			),
+			'/ then invalid query param and anchor'      => array(
+				'url'      => 'http://example.org/?param=value#anchor',
+				'expected' => 'http://example.org/#anchor',
+			),
+			'?#anchor when adding valid key/value args'  => array(
+				'url'      => 'http://example.org?#anchor',
+				'expected' => 'http://example.org?foo=bar#anchor',
+				'key'      => 'foo',
+				'value'    => 'bar',
+			),
+			'/?#anchor when adding valid key/value args' => array(
+				'url'      => 'http://example.org/?#anchor',
+				'expected' => 'http://example.org/?foo=bar#anchor',
+				'key'      => 'foo',
+				'value'    => 'bar',
+			),
+		);
+	}
+
 	/**
 	 * @ticket 21594
 	 */