diff --git a/scrapy/downloadermiddlewares/cookies.py b/scrapy/downloadermiddlewares/cookies.py
index 1f920fa2e..cc70fe366 100644
--- a/scrapy/downloadermiddlewares/cookies.py
+++ b/scrapy/downloadermiddlewares/cookies.py
@@ -52,12 +52,11 @@ class CookiesMiddleware:
         if not crawler.settings.getbool("COOKIES_ENABLED"):
             raise NotConfigured
         o = cls(crawler.settings.getbool("COOKIES_DEBUG"))
-        if crawler.settings.getbool("COOKIES_EXPOSE_JARS"):
-            crawler.signals.connect(o.spider_opened, signal=signals.spider_opened)
+        crawler.signals.connect(o.spider_opened, signal=signals.spider_opened)
         return o
 
     def spider_opened(self, spider: Spider) -> None:
-        spider.jars = self.jars
+        spider.cookie_jars = self.jars
 
     def _process_cookies(
         self, cookies: Iterable[Cookie], *, jar: CookieJar, request: Request