diff --git a/core/tests/Drupal/FunctionalTests/AssertLegacyTrait.php b/core/tests/Drupal/FunctionalTests/AssertLegacyTrait.php
index 8f24139..a08de40 100644
--- a/core/tests/Drupal/FunctionalTests/AssertLegacyTrait.php
+++ b/core/tests/Drupal/FunctionalTests/AssertLegacyTrait.php
@@ -219,14 +219,13 @@ protected function assertNoOption($id, $option) {
   /**
    * Passes if the internal browser's URL matches the given path.
    *
-   * @param \Drupal\Core\Url|string $path
-   *   The expected system path or URL.
+   * @param string $path
+   *   The expected system path.
    *
    * @deprecated Scheduled for removal in Drupal 9.0.0.
    *   Use $this->assertSession()->addressEquals() instead.
    */
   protected function assertUrl($path) {
-    $path = "/$path";
     $this->assertSession()->addressEquals($path);
   }
 
diff --git a/core/tests/Drupal/Tests/BrowserTestBase.php b/core/tests/Drupal/Tests/BrowserTestBase.php
index 867db61..ddfaf1b 100644
--- a/core/tests/Drupal/Tests/BrowserTestBase.php
+++ b/core/tests/Drupal/Tests/BrowserTestBase.php
@@ -554,7 +554,7 @@ public function getSession($name = NULL) {
    *   A new web-assert option for asserting the presence of elements with.
    */
   public function assertSession($name = NULL) {
-    return new WebAssert($this->getSession($name));
+    return new WebAssert($this->getSession($name), $this->baseUrl);
   }
 
   /**
diff --git a/core/tests/Drupal/Tests/WebAssert.php b/core/tests/Drupal/Tests/WebAssert.php
index da3a86d..ec31fdf 100644
--- a/core/tests/Drupal/Tests/WebAssert.php
+++ b/core/tests/Drupal/Tests/WebAssert.php
@@ -6,6 +6,7 @@
 use Behat\Mink\WebAssert as MinkWebAssert;
 use Behat\Mink\Element\TraversableElement;
 use Behat\Mink\Exception\ElementNotFoundException;
+use Behat\Mink\Session;
 use Drupal\Component\Utility\Html;
 
 /**
@@ -14,6 +15,42 @@
 class WebAssert extends MinkWebAssert {
 
   /**
+   * The absolute URL of the site under test.
+   *
+   * @var string
+   */
+  protected $baseUrl = '';
+
+  /**
+   * Constructor.
+   *
+   * @param \Behat\Mink\Session $session
+   *   The Behat session object;
+   * @param string $base_url
+   *   The base URL of the site under test.
+   */
+  public function __construct(Session $session, $base_url = '') {
+    parent::__construct($session);
+    $this->baseUrl = $base_url;
+  }
+
+  /**
+   * {@inheritdoc}
+   */
+  protected function cleanUrl($url) {
+    // Strip the base URL from the beginning for absolute URLs.
+    if ($this->baseUrl !== '' && strpos($url, $this->baseUrl) === 0) {
+      $url = substr($url, strlen($this->baseUrl));
+    }
+    // Make sure there is a forward slash at the beginning of relative URLs for
+    // consistency.
+    if (parse_url($url, PHP_URL_HOST) === NULL && strpos($url, '/') !== 0) {
+      $url = "/$url";
+    }
+    return parent::cleanUrl($url);
+  }
+
+  /**
    * Checks that specific button exists on the current page.
    *
    * @param string $button