Trained in Moscow by the Bolshoi ballet school, from which he graduated in 1924, Moiseyev was admired both as a character dancer and as a choreographer at the Bolshoi Theatre. In 1936 he was appointed head of the choreography department of the newly established Theatre of Folk Art in Moscow. After organizing a national folk dance festival, he founded (1937) the State Academic Folk Dance Ensemble, which featured 35 dancers, principally amateurs, and dances from the 11 republics then forming the U.S.S.R. Subsequently he built a company of about 100 professional dancers trained by either the Bolshoi Theatre School or its National Dance Department, which Moiseyev headed; all ensemble dancers have background in classical ballet.

Moiseyev's choreography often featured sequential geometric patterns performed with great precision. His work was especially admired, however, for the balance that it maintained between authentic folk dance and theatrical effectiveness. Thus, although the ensemble became famous for its spectacular and acrobatic leaps and jumps, Moiseyev's choreography consistently derived from what he called “root movements,” the basic steps characteristic of a particular type of folk dance. He created more than 170 dances for the ensemble, including Ukrainian Suite, portraying a young couple's betrothal; Soccer Dance, a comic version of this game; and the well-known Partisans, with its representations of guerrilla warfare and men on horseback. His Bulba so effectively re-created the folklore of Belorussia that it was adopted as that region's national dance. After 1955 the ensemble toured France, England, Egypt, Japan, and the United States; it continued to perform into the early 21st century.