The 35-year-old forward scored 21 points (five goals, 16 assists) in 57 games for the Dallas Stars last season after signing a one-year contract with them July 1, 2019.
"This opportunity came up, and it's something I didn't want to turn down," Perry said. "I always wanted to play in a Canadian city, and growing up, Montreal was my favorite team, being so close to the Quebec border in northern Ontario (New Liskeard). This is exciting for me. It's a new chapter, and I'm looking forward to it."
Perry scored nine points (five goals, four assists) in 27 games in the 2020 Stanley Cup Playoffs, including a goal in the second overtime to defeat the Tampa Bay Lightning in Game 5 of the Cup Final. The Stars lost the best-of-7 series in six games.
"Losing in Game 6 of a Stanley Cup Final, it just rips you apart," Perry said. "You're hungrier for more, and that's what this team is giving me. That's what I see in this team. I'm excited to be here, I'm excited to be a Canadien, and away we go. It's going to be fun."
Selected by the Anaheim Ducks in the first round (No. 28) of the 2003 NHL Draft, Perry has scored 797 points (377 goals, 420 assists) in 1,045 regular-season games and 98 points (41 goals, 57 assists) in 145 NHL playoff games.
Perry won the Stanley Cup with Anaheim in 2007 and is second in games (988; Ryan Getzlaf, 1,053) and goals (372; Teemu Selanne, 457), and third in assists (404) and points (776) in Ducks history. He was voted winner of the Hart Trophy as NHL MVP in 2010-11, when he also won the Maurice "Rocket" Richard Trophy by leading the NHL with 50 goals.
Michael Frolik agreed to a one-year, $750,000 contract with the Canadiens on Dec. 23. The forward played against Perry for several seasons while in the Western Conference with the Chicago Blackhawks, Winnipeg Jets and Calgary Flames.
"When he was in Anaheim, I saw him often," Frolik said. "He and Getzlaf, when they were in their prime, they were among the best in the League. I know he's great around the net, power play. ... You could see what he did in the playoffs for Dallas last year, scoring those big goals, being big around the net. I think that's what he brings. You can really use him on the power play in front of the net, and that's huge these days."
Perry and Frolik are the newest additions to the Canadiens, who brought in forwards Tyler Toffoli and Josh Anderson, defenseman Joel Edmundson and goalie Jake Allen this offseason.
"You've got some young guys, you've got some older guys, you've got one of the best goalies in the world in Carey Price," Perry said. "All those tangibles, putting the pieces together, and I hope I can come in and help this team and go on and try to win a Stanley Cup."
NHL.com staff writer Mike Zeisberger contributed to this report