The Dallas Stars assigned Avery to the American Hockey League team Tuesday and he practiced with the Hartford Wolf Pack in the morning.
"Dallas has given me a great opportunity to come and play here right now," Avery said at the Wolf Pack's practice facility in nearby Cromwell. "I'm just worrying about today and happy that I'm back playing. That's the important thing."
Avery hasn't played since his NHL suspension in December for making a crude remark about other hockey players dating his former girlfriends. He completed treatment in a league counseling program last weekend and cleared waivers Monday.
The 28-year-old player spent parts of two seasons in New York before signing a $15.5 million, four-year deal with Dallas. The Stars are the only NHL team without a primary affiliate and could have sent him to any willing team, with the Rangers the likliest destination. They have already said Avery won't return to the Stars.
Avery wasn't sure when his AHL stint would lead to an NHL return.
"Guidelines and timelines aren't in my plans right now," he said. "I just want to help these guys as much as I can and just play hard and have some fun."
For Avery to return to the NHL, the Stars would have to recall him from Hartford. Avery would then have to pass through re-entry waivers. Any team that claimed him would be responsible for half his contract, with the Stars paying the other half. The teams with the poorest records get the first chance at claiming him.
Avery is earning $3.5 million this season and has three more years left on the deal that pays him $4 million a season.
Avery thanked Rangers president and general manager Glen Sather for giving him the chance to resume his career. Dallas has sent a dozen players to seven other AHL teams this season, but Avery is the only one who has gone to Hartford.
"Sean was a good player for the Rangers during his time here and has worked extremely hard off the ice over the last two months," Sather said in a statement.
In Avery's season and a half with the Rangers, the club was 50-23-13 when he played and 24-35-9 when he was out of the lineup.
Avery hasn't appeared in the AHL since a three-game stint with the Manchester Monarchs during the 2003 playoffs. Hartford's next game is Wednesday night at home against the Manitoba Moose, and the Wolf Pack said he will not play.
"My head felt good," Avery said after Tuesday's practice. "My legs and my lungs felt a little behind."
Information from ESPN.com's Pierre LeBrun and The Associated Press was used in this report.