The Bears hired Marc Trestman, Montreal's coach the last five seasons, as head coach last week.
Last season, the Alouettes led the Canadian Football League in scoring, averaging about 27 points, and were among the leaders in touchdowns, passing and fewest sacks allowed.
Before joining Montreal in 2011, Meyer spent four seasons at Colorado State. He also had stints at North Carolina State, Florida State and Memphis. Meyer signed with the Arizona Cardinals in 1995 as an undrafted free agent, and played in the Arena Football League with the St. Louis Stampede.