The 34-year-old forward is in the final season of a two-year contract and could be an unrestricted free agent July 1. He was acquired by the Kings in a trade with the Ottawa Senators with defenseman Dion Phaneuf for forwards Nick Shore and Marian Gaborik on Feb. 13, 2018.
RELATED: [2018-19 NHL Trade Tracker]
Thompson has six points (four goals, two assists) in 53 games this season and 134 points (57 goals, 77 assists) in 672 NHL games with the Boston Bruins, New York Islanders, Tampa Bay Lightning, Anaheim Ducks, Senators, and Kings.
It is the second trade in three days for the Canadiens (31-18-7), who also acquired forward Dale Weise and defenseman Christian Folin from the Philadelphia Flyers for defenseman David Schlemko and forward Byron Froese on Feb. 9. Montreal holds the first wild card into the Stanley Cup Playoffs from the Eastern Conference, six points ahead of the Pittsburgh Penguins, and trails the Bruins by one point for third place in the Atlantic Division.
The Canadiens begin a three-game road trip against the Nashville Predators at Bridgestone Arena on Thursday (8 p.m. ET; FS-TN, TSN2, RDS, NHL.TV).
Los Angeles (23-27-5), which is eight points behind the Minnesota Wild for the second wild card into the playoffs from the Western Conference, traded defenseman Jake Muzzin to the Toronto Maple Leafs for the rights to defenseman Sean Durzi, forward Carl Grundstrom and a first-round pick in the 2019 draft on Jan. 28.
The Kings will conclude a season-long six-game road trip against the Washington Capitals at Capital One Arena on Monday (7 p.m. ET; NBCSWA, FS-W, NHL.TV).