Wallace was born on August 6, 1887, in London. After completing his musical training, he went to the United States, where he initially worked primarily on the West Coast as a conductor of theater orchestras and as an organist accompanying silent films. At the same time, he also made a name as a songwriter, writing tunes such as the popular "Hindustan". With the advent of the talking film era, he worked increasingly for Hollywood film studios in the 1930s.
In 1936 he joined Disney Studios, and quickly became one of the most important composers in the studio for short animated films. Wallace provided the music for more than 100 of these shorts. One of his best-known pieces is the song "Der Fuehrer's Face" from the 1942 Donald Duck propaganda cartoon. This parody of a Horst Wessel song was, mainly through the version by Spike Jones and His City Slickers, one of the biggest hits during the Second World War. Other shorts Wallace scored include "Ben and Me" (1953), about Benjamin Franklin and a mouse, and the Oscar-winning "Toot, Whistle, Plunk and Boom" (1953), the first cartoon to use the new Cinemascope process. In 1949 Wallace composed the music in the Disney film The Adventures of Ichabod and Mr. Toad.
Walt Disney also had Wallace score full-length films for the studios. His first big success was Dumbo (1941), for which he, together with Frank Churchill, won his first and only Oscar in 1942. He went on to score Cinderella, Alice in Wonderland, Peter Pan, and Lady and the Tramp. Characteristic of all these productions was the cooperation of several composers in the creation of the music. Wallace understood this and integrated leitmotiv-like elements from the individual songs into the film scores.
When the Disney studios began increasingly producing full-length films, Wallace also wrote scores for these. In Darby O'Gill and the Little People (1959), Wallace wrote not only the score but also set the Lawrence Edward Watkin-penned popular songs "Pretty Irish Girl" and "The Wishing Song". In Toby Tyler, or Ten Weeks with the Circus (1959), he appeared as an actor, playing the conductor of the circus band.
Starting with Seal Island (1948), Wallace also specialized in musical accompaniments for Disney documentaries, including nearly all the films for the "People and Places" series and some of the "True Life Adventures". The music of White Wilderness (1958) was even nominated for an Oscar in 1959, a rare event for a documentary film.
Overall, Wallace contributed music to nearly 150 Walt Disney productions. He remained active in the studio in Los Angeles until shortly before his death at the age of 76.