The 56-year-old had been thought to be the favorite for the position, and indeed Fox Sports' Jimmy Johnson first spoke of the hiring over the weekend.
Trestman, who has spent the last five years in the Canadian Football League, was known for his offensive prowess.
"He’s very articulate and he’s very organized – he’s one of the most organized people I’ve been around," Alouettes GM Jim Popp told SB Nation on Tuesday.
"He’s got that organizational skill set and I don’t doubt one bit that with his experience in the NFL he would be able to put together a great coaching staff together. He’s proven himself as a head coach at a professional level. You can call it what you want but on-hand training as a head coach and proof goes a long way, goes a real long way. You can’t replace that."
Trestman will be attempting to turn around a Bears team that finished the season with a 10-6 record, disappointingly missing the playoffs after a 7-1 start.
The Bears' offense lagged behind the NFL average, with passing being a key problem. Chicago quarterbacks passed for a 29th-ranked average of 184.9 yards per game in 2012.
Trestman, who served as a quarterbacks coach during multiple stops of his career as well as offensive coordinator to the high-powered Arizona offense, is likely expected to help bring an abrupt improvement to the Bears' offensive game.
Lovie Smith was fired by the Bears on Dec. 31. Seattle offensive coordinator Darrell Bevell and Indianapolis offensive coordinator Bruce Arians were also finalists.