Celestin was born in Napoleonville, Louisiana, to a Creole family, son of a sugar-cane cutter.

Eager for a better life, he worked as a cook for the Texas and Pacific Railway, saved up money and bought used musical instruments.

About 1910, he gained a job as leader of the house band at the Tuxedo Dance Hall on North Franklin St. on the edge of Storyville.

Playing in the Original Tuxedo Orchestra with Celestin over the years were such notables as trombonist Bill Mathews, pianist Octave Crosby, drummer Christopher Goldston, cornetist Joe Oliver, trumpeter Mutt Carey, clarinetist Alphonse Picou, bassist Ricard Alexis and trumpeter Louis Armstrong.

The new Tuxedo Brass Band proved tremendously popular and was hailed as a key New Orleans tourist attraction.

In 1953, Papa Celestin was filmed leading his band for the travelogue Cinerama Holiday (released in 1955).