The NBA team says it will not exercise its option on his contract for next season.
Triano will be retained as a consultant and a special assistant to president and general manager Bryan Colangelo.
The Raptors say the search for a new head coach will commence immediately.
There is no definitive timetable for the completion of the search process.
Triano, a native of Niagara Falls, Ont., guided the Raptors to a record of 87-142 during his time as head coach.