He was born in Paris, the illegitimate son of Gaétan Vestris and Marie Allard.

He was dubbed "le dieu de la danse", (the god of dance), a popular title bestowed on the leading male dancer of each generation (previous 'Gods of the Dance' included his father Gaétan and Gaétan's teacher, Louis Dupré).

He made his debut at the Paris Opéra (as had his mother, Marie Allard) in the third divertissement of the pastorale La Cinquantaine (written by Desfontaines-Lavallée and set to music by Jean-Benjamin de La Borde) in 1772 and was immediately recognized for his talent.

He was accepted as a regular member of the troupe in 1775, became a soloist in 1776, a "premier danseur" (principal dancer) in 1778, and finally he was appointed "premier sujet de la danse" (roughly corresponding to modern étoile) in 1780, holding this rank in the company for the next 36 years.

Both Armand and a cousin Charles Vestris, son of a brother of Auguste's, were also dancers.