diff -u b/core/modules/link/src/Plugin/migrate/process/FieldLink.php b/core/modules/link/src/Plugin/migrate/process/FieldLink.php
--- b/core/modules/link/src/Plugin/migrate/process/FieldLink.php
+++ b/core/modules/link/src/Plugin/migrate/process/FieldLink.php
@@ -20,6 +20,7 @@
    * {@inheritdoc}
    */
   public function __construct(array $configuration, $plugin_id, $plugin_definition, MigrationInterface $migration) {
+    $configuration += ['uri_scheme' => 'http://'];
     parent::__construct($configuration, $plugin_id, $plugin_definition);
     $this->migration = $migration;
   }
@@ -49,7 +50,7 @@
    */
   protected function canonicalizeUri($uri) {
     // If we already have a scheme, we're fine.
-    if (empty($uri) || !is_null(parse_url($uri, PHP_URL_SCHEME))) {
+    if (empty($uri) || !is_null(parse_url($uri, \PHP_URL_SCHEME))) {
       return $uri;
     }
 
@@ -87,12 +88,7 @@
         // Pattern specific to external links.
         $external_pattern = '/^' . $protocol . '?' . $authentication . '?(' . $domain . '|' . $ipv4 . '|' . $ipv6 . ' |localhost)' . $port . '?';
         if (preg_match($external_pattern . $end, $uri)) {
-          if (!empty($this->configuration['url_scheme']) && ($this->configuration['url_scheme'] === "https://")) {
-            return $this->configuration['url_scheme'] . $uri;
-          }
-          else {
-            return 'http://' . $uri;
-          }
+          return $this->configuration['uri_scheme'] . $uri;
         }
       }
     }
diff -u /dev/null b/core/modules/link/src/Plugin/migrate/process/d6/FieldLink.php
--- /dev/null
+++ b/core/modules/link/src/Plugin/migrate/process/d6/FieldLink.php
@@ -0,0 +1,91 @@
+<?php
+
+namespace Drupal\link\Plugin\migrate\process\d6;
+
+use Drupal\Core\Plugin\ContainerFactoryPluginInterface;
+use Drupal\migrate\Plugin\MigrationInterface;
+use Drupal\migrate\MigrateExecutableInterface;
+use Drupal\migrate\ProcessPluginBase;
+use Drupal\migrate\Row;
+use Symfony\Component\DependencyInjection\ContainerInterface;
+
+@trigger_error('FieldLink is deprecated in Drupal 8.4.x and will be removed before Drupal 9.0.x. Use \Drupal\link\Plugin\migrate\process\FieldLink instead.', E_USER_DEPRECATED);
+
+/**
+ * @MigrateProcessPlugin(
+ *   id = "d6_field_link"
+ * )
+ *
+ * @deprecated in Drupal 8.4.x, to be removed before Drupal 9.0.x. Use
+ * \Drupal\link\Plugin\migrate\process\FieldLink instead.
+ */
+class FieldLink extends ProcessPluginBase implements ContainerFactoryPluginInterface {
+
+  /**
+   * {@inheritdoc}
+   */
+  public function __construct(array $configuration, $plugin_id, $plugin_definition, MigrationInterface $migration) {
+    parent::__construct($configuration, $plugin_id, $plugin_definition);
+    $this->migration = $migration;
+  }
+
+  /**
+   * {@inheritdoc}
+   */
+  public static function create(ContainerInterface $container, array $configuration, $plugin_id, $plugin_definition, MigrationInterface $migration = NULL) {
+    return new static(
+      $configuration,
+      $plugin_id,
+      $plugin_definition,
+      $migration
+    );
+  }
+
+  /**
+   * Turn a Drupal 6 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) {
+    $attributes = unserialize($value['attributes']);
+    // Drupal 6 link attributes might be double serialized.
+    if (!is_array($attributes)) {
+      $attributes = unserialize($attributes);
+    }
+
+    if (!$attributes) {
+      $attributes = [];
+    }
+
+    // Massage the values into the correct form for the link.
+    $route['uri'] = $this->canonicalizeUri($value['url']);
+    $route['options']['attributes'] = $attributes;
+    $route['title'] = $value['title'];
+    return $route;
+  }
+
+}
diff -u b/core/modules/link/tests/src/Unit/Plugin/migrate/process/d6/FieldLinkTest.php b/core/modules/link/tests/src/Unit/Plugin/migrate/process/d6/FieldLinkTest.php
--- b/core/modules/link/tests/src/Unit/Plugin/migrate/process/d6/FieldLinkTest.php
+++ b/core/modules/link/tests/src/Unit/Plugin/migrate/process/d6/FieldLinkTest.php
@@ -2,11 +2,12 @@
 
 namespace Drupal\Tests\link\Unit\Plugin\migrate\process\d6;
 
-use Drupal\link\Plugin\migrate\process\FieldLink;
+use Drupal\link\Plugin\migrate\process\d6\FieldLink;
 use Drupal\Tests\UnitTestCase;
 
 /**
  * @group Link
+ * @group legacy
  */
 class FieldLinkTest extends UnitTestCase {
 
@@ -50,22 +51,6 @@
         'scheme:test',
         'scheme:test',
       ],
-      'Absolute URL with protocol prefix' => [
-        'http://www.google.com',
-        'http://www.google.com',
-      ],
-      'Absolute URL without protocol prefix' => [
-        'www.yahoo.com',
-        'http://www.yahoo.com',
-      ],
-      'Absolute URL without protocol prefix nor www' => [
-        'yahoo.com',
-        'http://yahoo.com',
-      ],
-      'Absolute URL with non-standard characters' => [
-        'http://www.ßÀÑÐ¥ƒå¢ë.com',
-        'http://www.ßÀÑÐ¥ƒå¢ë.com',
-      ],
     ];
   }
 
only in patch2:
unchanged:
--- a/core/modules/link/src/Plugin/migrate/field/d7/LinkField.php
+++ b/core/modules/link/src/Plugin/migrate/field/d7/LinkField.php
@@ -45,4 +45,15 @@ public function processFieldInstance(MigrationInterface $migration) {
     $migration->mergeProcessOfProperty('settings/title', $process);
   }
 
+  /**
+   * {@inheritdoc}
+   */
+  public function processFieldValues(MigrationInterface $migration, $field_name, $data) {
+    $process = [
+      'plugin' => 'field_link',
+      'source' => $field_name,
+    ];
+    $migration->mergeProcessOfProperty($field_name, $process);
+  }
+
 }
only in patch2:
unchanged:
--- a/core/modules/link/src/Plugin/migrate/process/d6/CckLink.php
+++ b/core/modules/link/src/Plugin/migrate/process/d6/CckLink.php
@@ -2,9 +2,9 @@
 
 namespace Drupal\link\Plugin\migrate\process\d6;
 
-@trigger_error('CckLink is deprecated in Drupal 8.3.x and will be removed before
-Drupal 9.0.x. Use \Drupal\link\Plugin\migrate\process\d6\FieldLink instead.',
-E_USER_DEPRECATED);
+use Drupal\link\Plugin\migrate\process\FieldLink;
+
+@trigger_error('CckLink is deprecated in Drupal 8.3.x and will be removed before Drupal 9.0.x. Use \Drupal\link\Plugin\migrate\process\FieldLink instead.', E_USER_DEPRECATED);
 
 /**
  * @MigrateProcessPlugin(
@@ -12,6 +12,6 @@
  * )
  *
  * @deprecated in Drupal 8.3.x, to be removed before Drupal 9.0.x. Use
- * \Drupal\link\Plugin\migrate\process\d6\FieldLink instead.
+ * \Drupal\link\Plugin\migrate\process\FieldLink instead.
  */
 class CckLink extends FieldLink {}
only in patch2:
unchanged:
--- /dev/null
+++ b/core/modules/link/tests/src/Unit/Plugin/migrate/process/FieldLinkTest.php
@@ -0,0 +1,84 @@
+<?php
+
+namespace Drupal\Tests\link\Unit\Plugin\migrate\process;
+
+use Drupal\link\Plugin\migrate\process\FieldLink;
+use Drupal\migrate\MigrateExecutableInterface;
+use Drupal\migrate\Plugin\MigrationInterface;
+use Drupal\migrate\Row;
+use Drupal\Tests\UnitTestCase;
+
+/**
+ * @group Link
+ */
+class FieldLinkTest extends UnitTestCase {
+
+  /**
+   * Test the url transformations in the FieldLink process plugin.
+   *
+   * @dataProvider canonicalizeUriDataProvider
+   */
+  public function testCanonicalizeUri($url, $expected, $configuration) {
+    $link_plugin = new FieldLink($configuration, '', [], $this->getMock(MigrationInterface::class));
+    $transformed = $link_plugin->transform([
+      'url' => $url,
+      'title' => '',
+      'attributes' => serialize([]),
+    ], $this->getMock(MigrateExecutableInterface::class), $this->getMockBuilder(Row::class)->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',
+        [],
+      ],
+      'Absolute URL with protocol prefix' => [
+        'http://www.google.com',
+        'http://www.google.com',
+        [],
+      ],
+      'Absolute URL without protocol prefix' => [
+        'www.yahoo.com',
+        'http://www.yahoo.com',
+        [],
+      ],
+      'Absolute URL without protocol prefix nor www' => [
+        'yahoo.com',
+        'https://yahoo.com',
+        ['uri_scheme' => 'https://'],
+      ],
+      'Absolute URL with non-standard characters' => [
+        'http://www.ßÀÑÐ¥ƒå¢ë.com',
+        'http://www.ßÀÑÐ¥ƒå¢ë.com',
+        [],
+      ],
+    ];
+  }
+
+}