diff --git a/core/modules/link/src/Plugin/migrate/process/d6/CckLink.php b/core/modules/link/src/Plugin/migrate/process/d6/CckLink.php
index 47c2f8b..663b9a3 100644
--- a/core/modules/link/src/Plugin/migrate/process/d6/CckLink.php
+++ b/core/modules/link/src/Plugin/migrate/process/d6/CckLink.php
@@ -37,6 +37,32 @@ public static function create(ContainerInterface $container, array $configuratio
   }
 
   /**
+   * Turn a Drupal 6 or 7 URI into a Drupal 8-compatible format.
+   *
+   * @param string $uri
+   *   The 'url' value from Drupal 6.
+   *
+   * @return string
+   *   The Drupal 8-compatible URI.
+   *
+   * @see \Drupal\link\Plugin\Field\FieldWidget\LinkWidget::getUserEnteredStringAsUri()
+   */
+  protected function canonicalizeUri($uri) {
+    // If we already have a scheme, we're fine.
+    if (empty($uri) || !is_null(parse_url($uri, PHP_URL_SCHEME))) {
+      return $uri;
+    }
+
+    // Remove the <front> component of the URL.
+    if (strpos($uri, '<front>') === 0) {
+      $uri = substr($uri, strlen('<front>'));
+    }
+
+    // Add the internal: scheme and ensure a leading slash.
+    return 'internal:/' . ltrim($uri, '/');
+  }
+
+  /**
    * {@inheritdoc}
    */
   public function transform($value, MigrateExecutableInterface $migrate_executable, Row $row, $destination_property) {
@@ -51,7 +77,7 @@ public function transform($value, MigrateExecutableInterface $migrate_executable
     }
 
     // Massage the values into the correct form for the link.
-    $route['uri'] = $value['url'];
+    $route['uri'] = $this->canonicalizeUri($value['url']);
     $route['options']['attributes'] = $attributes;
     $route['title'] = $value['title'];
     return $route;
diff --git a/core/modules/link/tests/src/Unit/Plugin/migrate/process/d6/CckLinkTest.php b/core/modules/link/tests/src/Unit/Plugin/migrate/process/d6/CckLinkTest.php
new file mode 100644
index 0000000..a96287a
--- /dev/null
+++ b/core/modules/link/tests/src/Unit/Plugin/migrate/process/d6/CckLinkTest.php
@@ -0,0 +1,56 @@
+<?php
+
+namespace Drupal\Tests\link\Unit\Plugin\migrate\process\d6;
+
+use Drupal\link\Plugin\migrate\process\d6\CckLink;
+use Drupal\Tests\UnitTestCase;
+
+/**
+ * @group Link
+ */
+class CckLinkTest extends UnitTestCase {
+
+  /**
+   * Test the url transformations in the CckLink process plugin.
+   *
+   * @dataProvider canonicalizeUriDataProvider
+   */
+  public function testCanonicalizeUri($url, $expected) {
+    $link_plugin = new CckLink([], '', [], $this->getMock('\Drupal\migrate\Plugin\MigrationInterface'));
+    $transformed = $link_plugin->transform([
+      'url' => $url,
+      'title' => '',
+      'attributes' => serialize([]),
+    ], $this->getMock('\Drupal\migrate\MigrateExecutableInterface'), $this->getMockBuilder('\Drupal\migrate\Row')->disableOriginalConstructor()->getMock(), NULL);
+    $this->assertEquals($expected, $transformed['uri']);
+  }
+
+  /**
+   * Data provider for testCanonicalizeUri.
+   */
+  public function canonicalizeUriDataProvider() {
+    return [
+      'Simple front-page' => [
+        '<front>',
+        'internal:/',
+      ],
+      'Front page with query' => [
+        '<front>?query=1',
+        'internal:/?query=1',
+      ],
+      'No leading forward slash' => [
+        'node/10',
+        'internal:/node/10',
+      ],
+      'Leading forward slash' => [
+        '/node/10',
+        'internal:/node/10',
+      ],
+      'Existing scheme' => [
+        'scheme:test',
+        'scheme:test',
+      ],
+    ];
+  }
+
+}
diff --git a/core/modules/migrate_drupal/tests/fixtures/drupal6.php b/core/modules/migrate_drupal/tests/fixtures/drupal6.php
index 4242cad..c123aeb 100644
--- a/core/modules/migrate_drupal/tests/fixtures/drupal6.php
+++ b/core/modules/migrate_drupal/tests/fixtures/drupal6.php
@@ -3402,9 +3402,9 @@
   'field_test_three_value' => '101.00',
   'field_test_identical1_value' => NULL,
   'field_test_identical2_value' => NULL,
-  'field_test_link_url' => 'http://www.example.com/buy-one-upon-a-time',
+  'field_test_link_url' => 'node/10',
   'field_test_link_title' => 'Buy it now',
-  'field_test_link_attributes' => 'a:1:{s:6:"target";s:6:"_blank";}',
+  'field_test_link_attributes' => 's:32:"a:1:{s:6:"target";s:6:"_blank";}";',
   'field_test_date_value' => NULL,
   'field_test_datestamp_value' => NULL,
   'field_test_datetime_value' => NULL,
diff --git a/core/modules/node/tests/src/Kernel/Migrate/d6/MigrateNodeTest.php b/core/modules/node/tests/src/Kernel/Migrate/d6/MigrateNodeTest.php
index 29bc9dc..76078dd 100644
--- a/core/modules/node/tests/src/Kernel/Migrate/d6/MigrateNodeTest.php
+++ b/core/modules/node/tests/src/Kernel/Migrate/d6/MigrateNodeTest.php
@@ -74,12 +74,19 @@ public function testNode() {
     $this->assertIdentical('test rev 3', $node->body->value);
     $this->assertIdentical('filtered_html', $node->body->format);
 
-    // Test that link fields are migrated.
+    // Test that a link field with an external link is migrated.
     $this->assertIdentical('http://groups.drupal.org/', $node->field_test_link->uri);
     $this->assertIdentical('Drupal Groups', $node->field_test_link->title);
     $this->assertIdentical([], $node->field_test_link->options['attributes']);
 
-    // Rerun migration with invalid link attributes and a different URL and
+    // Test that a link field with an internal link is migrated.
+    $node = Node::load(9);
+    $this->assertSame('internal:/node/10', $node->field_test_link->uri);
+    $this->assertSame('Buy it now', $node->field_test_link->title);
+    $this->assertSame(['attributes' => ['target' => '_blank']], $node->field_test_link->options);
+
+    // Rerun migration with two source database changes.
+    // 1. Add an invalid link attributes and a different URL and
     // title. If only the attributes are changed the error does not occur.
     Database::getConnection('default', 'migrate')
       ->update('content_type_story')
@@ -92,12 +99,27 @@ public function testNode() {
       ->condition('vid', '3')
       ->execute();
 
+    // 2. Add an leading slash to an internal link.
+    Database::getConnection('default', 'migrate')
+      ->update('content_type_story')
+      ->fields([
+        'field_test_link_url' => '/node/10',
+      ])
+      ->condition('nid', '9')
+      ->condition('vid', '12')
+      ->execute();
+
     $this->rerunMigration();
     $node = Node::load(2);
     $this->assertIdentical('https://www.drupal.org/node/2127611', $node->field_test_link->uri);
     $this->assertIdentical('Migrate API in Drupal 8', $node->field_test_link->title);
     $this->assertIdentical([], $node->field_test_link->options['attributes']);
 
+    $node = Node::load(9);
+    $this->assertSame('internal:/node/10', $node->field_test_link->uri);
+    $this->assertSame('Buy it now', $node->field_test_link->title);
+    $this->assertSame(['attributes' => ['target' => '_blank']], $node->field_test_link->options);
+
     // Test that we can re-import using the EntityContentBase destination.
     $title = $this->rerunMigration();
     $node = Node::load(2);