The Spanish international has signed a new four-and-a-half year contract, committing him to the Potters until the summer of 2020.
Bojan moved to the Britannia Stadium from Barcelona in the summer of 2014 and wasted little time in becoming a big crowd favourite, courtesy of a string of outstanding - and match-winning - displays.
He has overcome a serious knee injury sustained last season to re-establish himself in Mark Hughes' first team plans and, at the age of 25, has yet to reach his prime as a player which he hopes to do as a City player.
Chief Executive Tony Scholes said: "Bojan has made no secret of the fact that he now regards Stoke as his home in a football sense.
"When he joined us he made it clear that he wanted a period of stability in his career. It's obvious that he has found what he was looking for with us and we're understandably thrilled he has signed a long-term contract."
Bojan told stokecityfc.com: "I am very happy and motivated. Stoke City gave me the opportunity to play in the most competitive league in the world, the Premier League, and I have only words of gratitude for their trust and for the way they have treated me since the first day I arrived to England.
"Mark Hughes convinced me to come to Stoke, he has helped me and showed his trust in me from the beginning, he followed closely the recovery process from my injury and there is no doubt I have signed an extension of my contract thanks to him."
Bojan also paid tribute to the Club's supporters, insisting: "They always support me - on the pitch, when I was injured, every time I leave the stadium.
"They are passionate and I can proudly say that my team-mates and I feel their warmth and their support every single day. That is very important for me and encourage me to keep improving and trying to give my best."