The Ducks announced the hiring Friday.
Nonis was fired by the Maple Leafs in April after nearly 2 1/2 years in charge.
Toronto made the playoffs in 2014 for the first time since 2003, but regressed sharply this year. Nonis was swept out along with coach Peter Horachek by team president Brendan Shanahan.
Nonis was Vancouver's general manager from 2004-08. He worked there with Murray, who was a Canucks scout before moving to Anaheim as Brian Burke's vice president of hockey operations in 2005.
Nonis briefly worked with Burke and Murray in Anaheim in 2008 before following Burke to Toronto.