The 23-year-old has signed a four-year deal at the Britannia Stadium, with the Premier League club paying an undisclosed fee to sign the attacker from the Catalan giants
The 23-year-old becomes the Potters' fifth signing of the summer following the arrivals of Mame Biram Diouf, Steve Sidwell, Phil Bardsley and Dionatan Teixeira having arrived from Camp Nou for an undisclosed fee.
Manager Mark Hughes has hailed the signing of the Spaniard, telling the club's official website: "Anyone who knows European football will be aware of him as a player and the fact that he sees his future at Stoke City is really exciting and an endorsement of the club itself.
"He's desperate to prove himself in the Premier League and we're pleased to be able to offer him that platform."
Bojan scored 26 goals in over 120 appearances for Barcelona but spent last season on loan at Ajax, having fallen down the pecking order at Camp Nou.