The 26-year-old Drazenovic has 16 goals and 45 points in 46 games for the Falcons this season.
A native of Prince George, British Columbia, Drazenovic was originally signed by the Blue Jackets as an unrestricted free agent on July 1, 2011, after spending four seasons with the St. Louis organization. The 6-foot-1, 192-pounder was scoreless in three games with the Blues. He'll be making his Blue Jackets debut when the club plays at Los Angeles on Friday.
Drazenovic was drafted by new Columbus general manager Jarmo Kekalainen when he was in charge of amateur scouting for the Blues in 2005.