diff -u b/core/modules/system/tests/modules/js_webassert_test/js/js_webassert_test.js b/core/modules/system/tests/modules/js_webassert_test/js/js_webassert_test.js
--- b/core/modules/system/tests/modules/js_webassert_test/js/js_webassert_test.js
+++ b/core/modules/system/tests/modules/js_webassert_test/js/js_webassert_test.js
@@ -1,6 +1,6 @@
 /**
  * @file
- * Attaches the behaviors for the Field UI module.
+ *  Testing behavior for JSWebAssertTest.
  */
 
 (function ($, Drupal, drupalSettings) {
@@ -11,7 +11,7 @@
    * @type {Drupal~behavior}
    *
    * @prop {Drupal~behaviorAttach} attach
-   *   Adds behaviors to the field storage add form.
+   *   Makes changes in the DOM to be able to test the completion of AJAX in assertWaitOnAjaxRequest.
    */
   Drupal.behaviors.js_webassert_test = {
     attach: function (context) {
reverted:
--- b/core/tests/Drupal/FunctionalJavascriptTests/EntityReference/EntityReferenceAutocompleteWidgetTest.php
+++ a/core/tests/Drupal/FunctionalJavascriptTests/EntityReference/EntityReferenceAutocompleteWidgetTest.php
@@ -42,23 +42,6 @@
   }
 
   /**
-   * Waits for the jQuery autocomplete popup.
-   */
-  protected function waitOnAutocomplete($field_name) {
-    $autocomplete_field_name = "[name='" . $field_name . "[0][target_id]']";
-    $autocomplete_field_popup = 'jQuery(jQuery("' . $autocomplete_field_name . '").data("ui-autocomplete").menu.element).is(":visible")';
-    $this->assertJsCondition($autocomplete_field_popup);
-  }
-
-  /**
-   * Assert for the jQuery autocomplete result count.
-   */
-  protected function assertResultCount($count, $field_name) {
-    $autocomplete_field_name = "[name='" . $field_name . "[0][target_id]']";
-    $autocomplete_field_popup = 'jQuery(jQuery("' . $autocomplete_field_name . '").data("ui-autocomplete").menu.element).find("li").length === ' . $count;
-    $this->assertJsCondition($autocomplete_field_popup);
-  }
-  /**
    * Tests that the default autocomplete widget return the correct results.
    */
   public function testEntityReferenceAutocompleteWidget() {
@@ -83,11 +66,11 @@
     $autocomplete_field = $page->findField($field_name . '[0][target_id]');
     $autocomplete_field->setValue('Test');
     $this->getSession()->getDriver()->keyDown($autocomplete_field->getXpath(), ' ');
+    $assert_session->waitOnAutocomplete();
 
+    $results = $page->findAll('css', '.ui-autocomplete li');
-    // Assert Autocomplete Popup is shown.
-    $this->waitOnAutocomplete($field_name);
 
+    $this->assertCount(2, $results);
-    $this->assertResultCount(2, $field_name);
     $assert_session->pageTextContains('Test page');
     $assert_session->pageTextContains('Page test');
 
@@ -107,11 +90,11 @@
     $autocomplete_field = $page->findField($field_name . '[0][target_id]');
     $autocomplete_field->setValue('Test');
     $this->getSession()->getDriver()->keyDown($autocomplete_field->getXpath(), ' ');
+    $assert_session->waitOnAutocomplete();
 
+    $results = $page->findAll('css', '.ui-autocomplete li');
-    // Assert Autocomplete Popup is shown.
-    $this->waitOnAutocomplete($field_name);
 
+    $this->assertCount(1, $results);
-    $this->assertResultCount(1, $field_name);
     $assert_session->pageTextContains('Test page');
     $assert_session->pageTextNotContains('Page test');
   }
diff -u b/core/tests/Drupal/FunctionalJavascriptTests/JSWebAssert.php b/core/tests/Drupal/FunctionalJavascriptTests/JSWebAssert.php
--- b/core/tests/Drupal/FunctionalJavascriptTests/JSWebAssert.php
+++ b/core/tests/Drupal/FunctionalJavascriptTests/JSWebAssert.php
@@ -145,13 +145,10 @@
    * Waits for the jQuery autocomplete delay duration.
    *
    * @see https://api.jqueryui.com/autocomplete/#option-delay
-   *
-   * @deprecated in Drupal 8.3.x, will be removed before Drupal 9.0.0.
    */
   public function waitOnAutocomplete() {
     // Wait for the autocomplete to be visible.
-    $condition = "(jQuery('.ui-autocomplete:visible li').length > 0)";
-    return $this->session->wait(10000, $condition);
+    return $this->waitForElement('css', '.ui-autocomplete li');
   }
 
   /**