The operation was conducted by Dr. David Porter, a foot specialist based in Indianapolis, on Tuesday.
The Bulls have confirmed that Gibson has already begun his rehabilitation programme as they want him to be fit and healthy prior to the start of the 2015-16 season.
Gibson, who played 62 games this season, has had issues with his left ankle in the past and also revealed that he was playing with a stage 2 ligament tear in his hand in February.
Speaking about his ankle injury in February, Gibson had told reporters: "That's never going to go away. Doctors told me that's going to go away after the season is done. But I said, 'Doc, whatever it takes, just bandage me up. I'm going to get my treatment and do what I can out there on the court. No excuses. Try to help my team any way I can.'"
Gibson averaged 10.3 points, 6.4 rebounds, 1.1 assists and 1.2 blocks per game in the 2014-15 season.