Playfair was coaching Calgary's American Hockey League affiliate, the Abbotsford Heat, this past season.
Calgary had exercised the option year on Playfair's contract to coach the Heat again, but Playfair had a clause that allowed him to take another NHL job.
The Fort St. James, B.C., native spent 11 seasons coaching in the Flames organization.
In his one season as head coach in 2006-07, the Flames went 43-29-10. Calgary lost in the first round of playoffs to Detroit in six games.
Playfair held the title of associate coach after that as the Flames hired Mike Keenan and then Brent Sutter to coach the team.
The Coyotes announced Monday the club had signed Playfair to a multi-year deal. He'll work with current head coach Dave Tippett.
Flames general manager Jay Feaster said in a statement the Flames will start looking for a new head coach for Abbotsford immediately.