The Ducks announced the deal a few hours before their 5-2 victory over Philadelphia.
"He a guy who's going to play with some fire and he's going to force other people to get involved in the hockey game," Ducks coach Randy Carlyle said. "He has the ability to agitate at times, and he's proven that he can score 10-15 goals in this league and be responsible defensively. And that's what we're looking for."
Lapierre, 25, had eight points (5 goals, 3 assists) and minus-7 in 38 games this season. He had 15 goals and 28 points for Montreal in 2008-09, both career highs.
But he has expressed disappointment recently regarding his limited ice time and role with the team, according to a story on the Montreal Gazette website.
"Max has been with the Canadiens for a long time and it was time to move on," Habs general manager Pierre Gauthier told the Gazette. Gauthier was the Ducks' assistant general manager from 1993 to 1995, and rejoined them before the 1998-99 season as president and general manager.
Festerling, 24, has played only one game with the Ducks this season, after playing 42 games in Anaheim last season.
Pierre LeBrun covers the NHL for ESPN.com. Information from The Associated Press contributed to this report.