Moyes, Ellman and Gretzky joined to buy the team in 2001 for about US$125 million. Gretzky will continue to have a minority ownership in both ventures.
Moyes said it was his "full intention" to have Gretzky back as coach.
Gretzky, whose Hall of Fame playing career ended in 1999, had never coached in the NHL before taking over the Coyotes this season -- and it hasn't been an easy one.
"You couldn't ask to live and be in a better city or be in a better situation," Gretzky said. "But how long I was going to coach, I wasn't sure. But I will say this: I truly have enjoyed it much more than I probably anticipated when I started in September."
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