The 23-year-old broke into the Barca first team in 2007 but struggled to make an impression and moved to Roma for £10million before moving back to the Nou Camp last summer following a loan spell at AC Milan.
Another stint away from Catalunya quickly followed, as he spent the 2013/14 campaign in Holland with Ajax, and he will now be taking on a new challenge in England.
A statement issued through Stoke's official Twitter account read: "#HolaBojan Stoke City are delighted to confirm the signing of @BoKrkic from @FCBarcelona on a 4-year deal".
It is a major coup for manager Mark Hughes, who was spotted chatting to the Spaniard at Cheshire's Rookery Hall two weeks ago.
The Spanish international becomes the club's fifth signing of the summer following the acquisition of Mame Biram Diouf, Steve Sidwell, Phil Bardsley and Dionatan Teixeira.
A statement on the club's website read: "The signing of Bojan was completed this morning and he will now fly out to Germany where he will link-up with his new teammates at their training base in Reit im Winkl."
Hughes said: "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.
"The time he spends with the squad in Germany will help him settle in and will give myself and the coaches the chance to take a good look at him."
Bojan played in more than 120 league games for Barca, scoring 26 goals, and his performances encouraged comparisons to Lionel Messi before falling out of favour at the Nou Camp.
Stoke's chief executive Tony Scholes added: "We are delighted to have signed such a richly talented and exciting player, who is still only 23.
"A number of other clubs had expressed an interest in him but Bojan believes joining Stoke City will benefit his career and we have no doubts he will prove to be a wonderful addition to our squad.
"The signing of Bojan, along with the other players we have recruited ahead of the new season, underlines the progress we are making as a club."