The Flames are in rebuilding mode after missing the playoffs for a fourth straight season. Burke will report directly to president Ken King and general manager Jay Feaster will report to Burke.
Burke was fired as president and general manager of the Toronto Maple Leafs in January. He has been working as a part-time scout with the Anaheim Ducks since February.
The Flames also promoted John Bean from senior vice president, finance and administration to chief operating officer.
Source: Associated Press