Geronimi was born in Italy, immigrating to the United States as a young child. Geronimi's earliest work in the animation field was for the J.R. Bray Studios, where he worked with Walter Lantz. Geronimi left Bray in 1931 to join Walt Disney Studio, where he remained for the rest of his career. Geronimi started off in the shorts department, eventually becoming a director. His 1941 short, "Lend a Paw", won the Academy Award for Best Animated Short Subject.
Geronimi moved into directing feature-length animated films after the end of World War II. He served as a sequence director on The Three Caballeros, as well as individual segments of the package films of the late 1940s, among them Blame It on the Samba and Pecos Bill in Melody Time, and The Legend of Sleepy Hollow in The Adventures of Ichabod and Mr. Toad. After that, Geronimi became one of the directors on Cinderella, Alice in Wonderland, Peter Pan, Lady and the Tramp, Sleeping Beauty, and One Hundred and One Dalmatians.
After Geronimi left Disney in 1959, he worked in television for a number of years, including directing many episodes of the 1967 animated Spider-Man series. He retired from animation sometime in the late 1960s, and provided illustrations for children's books by Joan Pizzo.
Geronimi received the 1978 Winsor McCay Award from the International Animated Film Society, ASIFA-Hollywood, for his lifetime of contributions to the animation field. The award was presented by his long time friend and colleague Walter Lantz.
Geronimi died on April 24, 1989 at his home in Newport Beach, California. He was 87.