He lost his battle with lung cancer at his home in Albuquerque, New Mexico on 2 May, according to the Associated Press.
Wolfe, who was born in London, began performing comedy in England in the 1950s. He later moved to the U.S., where he landed roles in a number of hit TV shows, including I Dream of Jeannie, Bewitched, The Munsters and The Monkees.
The actor also voiced roles in animated movie The Jungle Book and Carey Grant's 1964 classic Father Goose, while his writing credits include Emmy Award-winning variety show Rowan & Martin's Laugh-In.
Wolfe went on to launch a 12-year teaching career at the University of New Mexico, specialising in screenwriting.