diff --git a/core/config/install/core.extension.yml b/core/config/install/core.extension.yml
index ce74bae..659446c 100644
--- a/core/config/install/core.extension.yml
+++ b/core/config/install/core.extension.yml
@@ -1,2 +1,3 @@
 module: {}
 theme: {}
+profile: ''
diff --git a/core/config/schema/core.extension.schema.yml b/core/config/schema/core.extension.schema.yml
index bdc84b9..087e2e3 100644
--- a/core/config/schema/core.extension.schema.yml
+++ b/core/config/schema/core.extension.schema.yml
@@ -14,3 +14,6 @@ core.extension:
       sequence:
         type: integer
         label: 'Weight'
+    profile:
+      type: string
+      label: 'Install profile'
diff --git a/core/includes/install.core.inc b/core/includes/install.core.inc
index 2d1765c..6e9636f 100644
--- a/core/includes/install.core.inc
+++ b/core/includes/install.core.inc
@@ -2197,12 +2197,6 @@ function install_write_profile($install_state) {
     // The user will have chosen.
   }
 
-  // Ensure to also store the installation profile in configuration for later
-  // use.
-  \Drupal::configFactory()->getEditable('core.extension')
-    ->set('profile', $install_state['parameters']['profile'])
-    ->save();
-
   if ($settings_value == '' && $distribution && !is_writable(\Drupal::service('site.path') . '/settings.php')) {
     $need_to_write = FALSE;
   }
diff --git a/core/includes/install.inc b/core/includes/install.inc
index 22067c6..6a4070c 100644
--- a/core/includes/install.inc
+++ b/core/includes/install.inc
@@ -621,6 +621,12 @@ function drupal_install_system($install_state) {
   // Install base system configuration.
   \Drupal::service('config.installer')->installDefaultConfig('core', 'core');
 
+  // Ensure to also store the installation profile in configuration for later
+  // use.
+  \Drupal::configFactory()->getEditable('core.extension')
+    ->set('profile', $install_state['parameters']['profile'])
+    ->save();
+
   // Install System module and rebuild the newly available routes.
   $kernel->getContainer()->get('module_installer')->install(array('system'), FALSE);
   \Drupal::service('router.builder')->rebuild();
diff --git a/core/lib/Drupal/Core/Config/ExtensionInstallStorage.php b/core/lib/Drupal/Core/Config/ExtensionInstallStorage.php
index e18c63b..96e1e38 100644
--- a/core/lib/Drupal/Core/Config/ExtensionInstallStorage.php
+++ b/core/lib/Drupal/Core/Config/ExtensionInstallStorage.php
@@ -51,7 +51,7 @@ class ExtensionInstallStorage extends InstallStorage {
    *   (optional) Whether to include the install profile in extensions to
    *   search and to get overrides from.
    */
-  public function __construct(StorageInterface $config_storage, $profile,  $directory = self::CONFIG_INSTALL_DIRECTORY, $collection = StorageInterface::DEFAULT_COLLECTION, $include_profile = TRUE) {
+  public function __construct(StorageInterface $config_storage, $profile, $directory = self::CONFIG_INSTALL_DIRECTORY, $collection = StorageInterface::DEFAULT_COLLECTION, $include_profile = TRUE) {
     parent::__construct($directory, $collection);
 
     $this->configStorage = $config_storage;
diff --git a/core/modules/system/system.install b/core/modules/system/system.install
index ed181f2..be05e16 100644
--- a/core/modules/system/system.install
+++ b/core/modules/system/system.install
@@ -1647,3 +1647,21 @@ function system_update_8014() {
 /**
  * @} End of "addtogroup updates-8.0.0-rc".
  */
+
+/**
+ * @addtogroup updates-8.3.x
+ * @{
+ */
+
+/**
+ * Add install profile to core.extension configuration.
+ */
+function system_update_8300() {
+  \Drupal::configFactory()->getEditable('core.extension')
+    ->set('profile', \Drupal::installProfile())
+    ->save();
+}
+
+/**
+ * @} End of "addtogroup updates-8.3.x".
+ */