Therrien's return is the latest move in a bid by one of the league's most storied franchises to regain its former glory, Marc Bergevin having been appointed general manager last month in place of Pierre Gauthier.
The Canadiens finished dead last in the Eastern Conference and missed the playoffs this season for the first time since 2007. They have won the Stanley Cup a record 24 times but not since 1993.
Montreal native Therrien, a former defenseman who played 20 seasons in the NHL, coached the Canadiens from 2000 until he was replaced by Claude Julien in 2003, finishing with a 77-77-36 record.
He went on to coach the Pittsburgh Penguins from 2005 until 2009, leading them into the playoffs in 2007 and to the Eastern Conference championship title in 2008.
Pittsburgh lost the 2008 Stanley Cup Finals to the Detroit Red Wings in six games, finishing the playoffs with a 14-6 record.
Therrien's appointment ended weeks of speculation over Cunneyworth's successor with former NHL coach Marc Crawford and former Canadiens goaltender Patrick Roy reportedly among the candidates.
The English-speaking Cunneyworth, who was named to the job last December by Gauthier, touched off a firestorm in Montreal among the team's many French-speaking fans because he did not speak Quebec's official language.