"Our entire organization wishes each of them good luck in their future endeavours, and we sincerely thank them for their contributions to this franchise," Jeff Shumway, the Coyotes chief executive officer, said in a statement. "The organization will conduct a complete and thorough search for a general manager."
The Coyotes finished last in the Western Conference this season with a 31-46-5 record, missing the playoffs for the fourth straight season.
Barnett became Coyotes GM in August 2001, leaving the player agency business. He was Gretzky's longtime agent.
Fletcher joined the Coyotes in February 2001. Inducted into the Hockey Hall of Fame in 2004, Fletcher was GM of the Toronto Maple Leafs from 1991 to 1997 following 19 years as GM with the Calgary Flames.
Gilman had served 13 seasons with the Coyotes - previously Winnipeg Jets - organization.