The one-year deal will pay Beauchemin $1 million and contains $500,000 in potential performance bonuses, according to TVA Sports.
Beauchemin, 37, previously played for the Ducks from 2005 to 2009 and 2011 to 2015 before spending the past two seasons with the Colorado Avalanche. He won a Stanley Cup with Anaheim in 2007.
He became a free agent in June when the Avalanche, looking to free up a protection spot ahead of the expansion draft, bought out the final year of his contract.
Beauchemin, 37, had a cap hit of $4.5 million, and his no-movement clause would have necessitated the Avs protecting him. By exercising the $1.5 million buyout, they were able to shield a younger player from the Vegas Golden Knights.
In his second season with Colorado, Beauchemin had five goals and 13 assists. He has posted 73 goals and 198 assists in 836 career NHL games and has also played for the Montreal Canadiens, Columbus Blue Jackets and Toronto Maple Leafs.