He began as an employee of the Walt Disney Studios. He started as an animator in the short Modern Inventions (released on May 29, 1937). After thirteen films as an animator, he was assigned as a writer, beginning with Donald's Nephews (released on April 15, 1938). He was given writing credits for 21 films.
In 1942 he helped Carl Barks create his first two comic book stories, Pluto Saves the Ship and Donald Duck Finds Pirate Gold. Unlike Barks he did not leave the Studio after this and he was finally assigned as the director of his films. The short Donald's Off Day (released on December 8, 1944) was the first of 94 films he would direct. His production includes most of the shorts featuring Donald Duck, Chip 'n Dale and Humphrey the Bear, although he also directed some shorts starring Goofy or minor Walt Disney characters. Besides that he also directed a number of films for Walter Lantz's Studio featuring both Woody Woodpecker and a number of minor characters. After Disney stopped producing animated shorts Hannah moved to the Lantz Studio on a more permanent basis. Besides directing shorts he was also assigned as Assistant Director in the TV series Woody Woodpecker Show, which started airing on October 3, 1957. His last directing effort was the short Charlie's Mother-In-Law (released on April 16, 1963). After this he retired.
He was honored as a "Disney Legend" in 1992. As Carl Barks is credited with creating the personality of Donald Duck's comic book version, Jack Hannah is credited with developing, if not creating, the personality of the animated version.