The Oilers were looking for a center who can win faceoffs. Desharnais is winning 47.8 percent of his faceoffs this season and was at 48.7 percent last season, but at 52.9 percent in 82 games in 2014-15.
"I know we have been deficient in that area this year," Chiarelli said. "He's perennially strong. I know this year he hasn't played as much, but he's a smart faceoff man and that obviously played into the equation."
Desharnais was last used regularly as a top-six center in 2014-15, getting 48 points (14 goals, 34 assists) in 82 games. He had 10 points (four goals, six assists) in 31 games for Montreal this season, and 250 points (79 goals, 171 assists) in 435 NHL games, all with the Canadiens.
Chiarelli saw a lot of Desharnais at his best as general manager of the Boston Bruins from 2006-15, particularly in the Stanley Cup Playoffs in 2011 and 2014.
"We looked at a lot of different players and this is player that you check a lot of the boxes with him," Chiarelli said. "He's got playoff experience, he's a very smart player, smart without the puck. I'd seen a lot of him in Ottawa and seen a lot of him in Boston and he's a very competitive player. I know he's undersized (5-foot-7, 171 pounds) but he's strong on the puck."
Davidson, 25, is the second left-shooting defenseman the Canadiens added in a little more than 24 hours following the acquisition Monday of Jordie Benn in a trade with the Dallas Stars for defenseman Greg Pateryn and a fourth-round pick in the 2017 NHL Draft.
Davidson had 13 points (five goals, eight assists) in 91 NHL games for Edmonton over the past three seasons. He played an average of 15:23 per game this season, the lowest average ice time of any Oilers defenseman who has played more than 10 games.
Defenseman Darnell Nurse on Tuesday played his second game for the Oilers since returning from an ankle injury. The NHL Trade Deadline is Wednesday at 3 p.m. ET.
"There's a lot of times that I've seen and been part of at the deadline where teams add a lot of players and you mix up the chemistry," Chiarelli said. "… This team deserved to be attended to and we've done that. I know we subtracted a defenseman, but we do have deep [defense], so if we do nothing tomorrow, I'm perfectly fine with it."