Financial details of the contract were not disclosed.
Lemieux, 35, helped New Jersey to its second title last season, and is second to Wayne Gretzky with 19 game-winning goals in the playoffs. He also was a member of New Jersey's 1995 championship team, and helped Montreal (1986) and Colorado (1996) to titles.
Lemieux donned a Coyotes jersey with his familiar No. 22 at a news conference hours before Phoenix faced the Dallas Stars at America West Arena.
"I thought I'd be standing up here in July. It's been a long wait. It's been very difficult for everybody," said Lemieux. "Hopefully I can move forward and start playing again."
Lemieux has 345 goals, 353 assists and 1,584 penalty minutes in 1,001 games. He has 80 goals and 77 assists in 221 playoff games.
Lemieux said he hoped to be in uniform for Wednesday night's home game against Vancouver.
Coyotes general manager Bobby Smith "is going to let it be my call," Lemieux said. "I need to get on the ice and see how I feel. I've been working out on my own but it's not quite the same as a game."
Lemieux has been training at the Coyotes' practice facility in Scottsdale since last month as he waited for Hall of Famer Wayne Gretzky and Phoenix developer Steve Ellman to work out final details to buy the Coyotes from current owner Richard Burke.
That $87 million dollar deal now is expected to close in mid-December.
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