The Blue Jackets were battling with St. Petersburg SKA of the KHL, who pitched an offer to Bobrovsky believed to be worth $10 million per season.
Bobrovsky posted a 21-11-6 record with a 2.00 goals-against-average, a .932 save percentage and four shutouts in 38 games with the Blue Jackets this past season.
Based on his performence this year, Bobrovsky was awarded the Vezina Tropy, given to the NHL's top goaltender.
The Blue Jackets acquired Bobrovsky on June 22, 2012 from the Philadelphia Flyers in exchange for a second-round and fourth-round pick in 2012 and a fourth-round pick in 2013.
The deal between the Blue Jackets and Bobrovsky is expected to be signed as early as Sunday night, with a formal announcement expected shortly after the contract is officially signed.