Shawcross has made remarkable progress since leaving United in 2008 and is now on the fringes of the England squad.
The 23-year-old has been a target for Liverpool and Tottenham in the last 18 months but insists he is happy to remain a Potter now they are competing in the Europa League.
"I've always said that I wanted to play in Europe and Stoke have given me that opportunity," he said, "so my future is undoubtedly here at the Britannia Stadium.
"I really do love it here, the fans are great to me and the manager is absolutely top class.
"He [Pulis] is probably the biggest factor in [my] wanting to be here because I really enjoy working under him. He keeps making me a better player and has shown unbelievable faith in me.
"With the group of lads we have here, I don't think anyone would want to leave.
"It's a great set-up, with a very good team who are all striving to bring success to Stoke."