Hannah was born January 15, 1913, in Nogales, Arizona. He moved to Los Angeles in 1931 to study at the Art Guild Academy. One of his first jobs was designing movie posters for Hollywood theaters. In 1933, during the Great Depression, Hannah dropped off his portfolio at Walt Disney Studios, and soon afterward was hired as an in-between and clean-up artist, working on Mickey Mouse, Donald Duck, and Silly Symphony cartoons. In 1975, Hannah was one of the co-founders, along with T. Hee, of the Character Animation program at the California Institute of the Arts.