Ott, 34, is on a one-year, $800,000 contract he signed July 1 and can become an unrestricted free agent, according to CapFriendly.com.
"It's obviously tough. It's mixed feelings. But it's part of the business," Ott said. "I absolutely loved the opportunity I got here in Detroit, to say the least. That Red Wing jersey meant a lot to me and it meant a lot to my family to be able to play in front of friends and family every single night as a Red Wing. But the business-wise, it's definitely part of it. I'm heading to a good team with another great heritage, so it's very exciting now to know that I have a chance in the [Stanley Cup Playoffs]."
Ott had six points (three goals, three assists) in 43 games with Detroit and was tied for second among Red Wings forwards with 1:57 of shorthanded time on ice per game, an area where the Canadiens have struggled and one general manager Marc Bergevin was trying to address. Benn led the Stars in shorthanded ice time and was used with Shea Weber on the first penalty-kill unit in a 1-0 win against the Columbus Blue Jackets on Tuesday.
Ott has a deserved reputation as an agitator, giving the Canadiens three such players with forwards Andrew Shaw and Brendan Gallagher. Ott won 58 percent of his faceoffs this season, leading the Red Wings. He was the least-used Detroit player at even strength (8:24 per game).
"He's one of the best teammates I've ever had around," Detroit coach Jeff Blashill said. "He's an excellent teammate. You can't say enough about him in the locker room and what he does from a leadership standpoint."
Ott has 287 points (109 goals, 178 assists) in 837 NHL games with the Dallas Stars, Buffalo Sabres, St. Louis Blues and Red Wings, and eight points (three goals, five assists) in 55 Stanley Cup Playoff games.
Davidson, 25, was the second left-shooting defenseman the Canadiens added in a little more than 24 hours following the acquisition of Benn for defenseman Greg Pateryn and a fourth-round pick in the 2017 NHL Draft.
"It's going to give us depth on defense," Montreal coach Claude Julien said. "It also creates internal competition. At this time of year, you never have enough players to protect yourselves. We know that injuries are a part of the game. We want to make sure we have depth and good competition as well."
Davidson had 13 points (five goals, eight assists) in 91 NHL games for Edmonton over the past three seasons, with one assist in 28 games this season playing 15:23 per game.
He has one year remaining on his contract at a salary cap charge of $1.425 million before he would become a restricted free agent, according to CapFriendly.com.
NHL.com correspondent Kevin Woodley contributed to this report.
