Trestman, the Montreal Alouettes head coach for five seasons and CFL coach of the year in 2009, replaces Lovie Smith, who was fired after nine seasons as head coach, a release from the team said.
Trestman, 57, spent 17 years as an offensive coordinator and position coach, working to mold quarterbacks with the Cleveland Browns, San Francisco 49ers, the Detroit Lions, the Arizona Cardinals and the Oakland Raiders.
"The skill set that Marc has, being an offensive mind, and then his great relationships that he's had with quarterbacks historically in the NFL and the work he's done with them makes him a good fit for the job," Alouettes general manager Jim Popp said.
The Bears interviewed at least 13 candidates for the position, including Colts offensive coordinator Bruce Arians and Seahawks offensive coordinator Darrell Bevell, the Chicago Tribune reported.
General Manager Phil Emery's final decision reportedly came down to between Trestman and Arians.