The New York Rangers claimed Avery off re-entry waivers on Tuesday and is expected to be in their lineup against the Islanders on Thursday.
The Stars and Rangers will now split Avery's salary and cap cost for the duration of his contract, which runs through the 2012 season.
The Stars will pay about $386,000 of Avery's remaining salary this season and $2 million each of the next three seasons. The Stars will take a cap hit of $1.9375 million each of the next three seasons as well.
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"It's just something we need to get behind us and move ahead," Stars Co-GM Les Jackson said Sunday during an interview on the Stars broadcast network. "That situation is going to linger with us for a couple years, but it is what it is. I wish it wasn't ours, but it is."
Avery was suspended for six games by the league after referring to ex-girlfriend Elisha Cuthbert, current girlfriend of Calgary's Dion Phaneuf, as his "sloppy seconds" after a morning skate in Calgary during Dallas' road trip in early December.
Avery was then placed in a league-mandated counseling program for anger management.
This will be Avery's second tour in New York, where he played 86 games from 2007 to 2008.