The 29-year-old has signed a two-year contract with the Premier League club and will link up with his new team-mates in France.
The club said on their Twitter feed: “#SCFC are delighted to announce the signing of Dutch international winger Ibrahim Afellay.”
Afellay arrives at the Britannia Stadium after his contract with Barcelona expired over the course of the summer.
Capped 50 times by the Netherlands, he joins fellow countrymen Erik Pieters and Marco van Ginkel in the Stoke squad, along with former Barcelona team-mates Bojan Krkic, Marc Muniesa and Moha El Ouriachi.
Potters chief executive Tony Scholes told his club’s official website: “It’s no secret that Ibrahim was wanted by a number of clubs and we are understandably delighted that he has chosen to join us.
“He’s clearly excited about the prospect of playing in the Premier League and the fact that he knows so many players who are already at the club will no doubt help him settle into his new surroundings.”
Afellay, who has flown to Stoke’s pre-season training camp in Evian, started his career with PSV Eindhoven.
He won a whole host of honours during his time with Barcelona – including the Champions League – although his time at the Nou Camp was disrupted by injury problems. He made just 21 league appearances for the club and had loan spells with Schalke and Olympiacos.
He becomes Stoke’s eighth close-season signing following the arrivals of Philipp Wollscheid, Jakob Haugaard, Joselu, Van Ginkel, Glen Johnson, Shay Given and Moha.