Wolf was born in New York City. His career in animation started in 1924, when he began work as an inker on Paramount Studios' Krazy Kat silent shorts. He moved to Fleischer Studios shortly afterwards, providing artwork for both the Koko the Clown and Betty Boop series. It was at Fleischer Studios that he met Shamus Culhane and Al Eugster, with whom he would maintain a long personal and professional relationship. The three would leave Fleischer to work briefly for Ub Iwerks, where they worked alongside Grim Natwick.
In 1938 Wolf, along with Eugster and Culhane, moved to Walt Disney Studios. After working briefly in the shorts department, Wolf moved on to features. He was one of the animators of Jiminy Cricket in Pinocchio, and the Centaurs in Fantasia. His final work at Disney was on Dumbo.
Wolf left Disney after the 1941 strike. He briefly provided uncredited work for Tex Avery at MGM before being drafted during World War II. Wolf was assigned to the First Motion Picture Unit, a group of former Hollywood personnel who created short educational films for the American military.
After the end of the war, Wolf worked briefly for animator Rudolph Ising before forming his own company, Animedia Inc. Animedia produced animation for advertising and commercial films. The company also designed some of the costumes used at Walt Disney World, as well as animating segments for Sesame Street.
Wolf folded Animedia in the 1970s in order to return to animation full time. He produced several animated features for Hanna Barbera, including 1987's The Jetsons Meet the Flintstones. He retired from animation in the 1980s, but continued to provide freelance commercial design, including developing mascots for the MGM Grand hotel in Las Vegas. Wolf died in 2006 at the age of 95.