Shawcross joined the Potters initially on loan in the summer of 2007 from Manchester United but made the move permanent in January 2008, helping them to Premier League promotion the same season.
The 33-year-old was named Stoke captain in 2010 and skippered the side to an FA Cup final in 2011, losing to Manchester City.
After making over 400 appearances for Stoke, Shawcross has terminated his contract, which would have expired this summer, and is set to join Phil Neville’s side in North America.
"Ryan's contribution to the Club over the last 14 years simply cannot be overstated. His outstanding leadership and the consistency of his displays made him a talismanic figure for us," Stoke chief executive Tony Scholes said in a statement.
"He feels the time is right to explore new opportunities and leaves with our very best wishes. I would like to take this opportunity to wish Ryan, his wife Kath and their family every success for the future - they will always be welcome at the bet365 Stadium."
Shawcross, lost his place in the Stoke team this season and made just two championship appearances.
"It's very rare these days for a player to stay at one club for 14 years; I'm sure Ryan has had opportunities to go elsewhere down the years but he clearly felt settled and valued here," Stoke manager Michael O'Neill added.
"He hasn't figured as often as he would have liked over the past couple of years but his professionalism and the way he has conducted himself, both on the training ground and around the club, since I joined simply cannot be questioned."
