Moore, 29, has 8 goals and 9 assists for 17 points in 48 games for Florida. He signed with the Panthers as a free agent just before the start of the season.
The Canadiens will be Moore's seventh NHL team, and this marks the third year in a row that he's has changed teams in midseason. He was claimed off waivers from Minnesota by Toronto in 2007-08, and was traded from Toronto to Buffalo at last season's trade deadline.
Moore was originally drafted by the New York Rangers in the third round in 2000.