Bigard was born in New Orleans on March 3, 1906, and studied music and clarinet with Lorenzo Tio. Moved to Chicago in the early 1920s, and played with "King" Joe Oliver, then to New York City where he joined Duke Ellington's Orchestra, where he stayed from 1927 through 1942. Moved to Los Angeles, California and did sound track work, then joined Kid Ory's band. In the 1950s and early 1960s he was with Louis Armstrong's All Stars. Bigard died in Los Angeles on June 27, 1980.
Bigard wrote an autobiography entitled "With Louis And The Duke". He is credited as composer or co-composer on several numbers, notably "Mood Indigo".