Terms of the deal were not disclosed.
Blue Jackets general manager Jarmo Kekalainen had termed re-signing the 24-year-old Russian as his top objective but the two sides had made little headway until just before the start of the NHL draft on Sunday.
Acquired from Philadelphia for draft picks last summer, Bobrovsky blossomed in Columbus. He had a 21-11-6 record with a 2.00 goals-against average, a .932 save percentage and four shutouts.
His stellar play fueled the Blue Jackets' 19-5-5 finish that brought them close to a playoff spot.