The Scotland international will to move to the bet365 Stadium at the end of his West Brom contract on 1 July, having captained the Baggies during his time at The Hawthorns, and is looking forward to the challenge ahead.
“It’s all happened incredibly quickly, but I am delighted to be here,” he told stokecityfc.com after signing a two-year deal.
“This is a fantastic club with a top manager and a great group of players and I am really looking forward to this opportunity.”
“I believe that his experience and leadership qualities will significantly enhance us.”
Fletcher, a five-time Premier League champion, has made 314 appearances during his top-flight career.
The 33-year-old could make his first outing in a Stoke shirt when his new club visit Sheffield United on 25 July in their first confirmed summer friendly.