Therrien, 48, coached Montreal from November 2000 through January 2003, helping the team to a playoff berth in the only full season (2001-02) he was behind the bench. The Canadiens are 77-77-36 under Therrien.
He'll replace Jacques Martin, who was fired 32 games in the last season and interim coach Randy Cunneyworth. The Canadiens were 31-35-16 in 2011-12 and missed in the playoffs for the first time in five years and had an Eastern Conference-low 78 points.
Montreal also brought in Marc Bergevin as general manager.
In addition to coaching Montreal, Therrien coached the Pittsburgh Penguins from December 2005-February 2009. The Penguins reached the Stanley Cup finals, losing to Detroit, with Therrien as coach in 2008. He was 135-105-32 with Pittsburgh.