The team first announced on Thursday that Bogosian would be undergoing the surgery to repair the injury after he started to feel discomfort during his offseason training.
The timetable for his return is expected to be four-to-six months.
"We are pleased the procedure on Zach's right wrist was successful this morning," said Jets general manager Kevin Cheveldayoff, via the Winnipeg Free Press.
"This wrist has been an issue which has troubled him for the past couple of seasons dating back to his time in Atlanta and forced him to miss games with the Jets last season. After resuming his on-ice training earlier this month, the wrist problem flared up again to the point surgery was deemed the best option by both Dr. MacDonald and Dr. Graham."
The No. 3 overall pick in the 2008 NHL draft, Bogosian appeared in 65 games for the Jets this past season and scored five goals to go with 25 assists. Offensively it was his best season in the NHL while spending most of his time playing alongside fellow defenseman Marc Stuart.
He's entering the final year of a two-year contract that pays him an average anual salary of $2.5 million.