The 33-year-old club legend was contracted until the end of this season, but that contract has now been cancelled, leaving him free to move to Major League Soccer in North America.
Shawcross signed from Manchester United in August 2007, initially on loan.
He then completed a £1m move from Old Trafford the following January.
Stoke boss O'Neill, who had already given him his blessing to move on, said: "Before I came to Stoke City the one player you immediately associated with the club when it came up in conversation was Ryan, simply because of the length of time he spent here.
"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.
"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.
Stoke chief executive Tony Scholes added: "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. He has been an outstanding role model, both on and off the pitch."