Dunayevsky was born to a Jewish family in Lokhvitsa, Poltava Governorate, Russian Empire in 1900. He studied at the Kharkov Musical School in 1910 where he studied violin under Konstanty Gorski and Joseph Achron. During this period he started to study the theory of music under Semyon Bogatyrev (1890–1960). He graduated in 1919 from the Kharkov Conservatory. At first he was a violinist, the leader of the orchestra in Kharkov. Then he started a conducting career. In 1924 he went to Moscow to run the Theatre Hermitage. In 1929 he worked for the first time for a music hall ("To the icy place") with Moscow music hall. Later, he worked in Leningrad (1929–1941) as a director and conductor of the Saint Petersburg music hall (1929–34), and then moved to Moscow to work on his own operettas and film music.
Dunayevsky wrote 14 operettas, 3 ballets, 3 cantatas, 80 choruses, 80 songs and romances, music for 88 plays and 42 films, 43 compositions for light music orchestra and 12 for jazz orchestra, 17 melodeclamations, 52 compositions for symphony orchestra and 47 piano compositions and a string quartet.
He was one of the first composers in the Soviet Union to start using jazz. His music was accessible to the masses, with melodious and memorable tunes that secured his success. He wrote the music for three of the most important films of the pre-war Stalinist era, Jolly Fellows, Circus and the film said to be Stalin's favourite film Volga-Volga, all directed by Grigori Aleksandrov.
In a reply to the British book The World of Music, he listed the following as his chief works: The Golden Valley operetta (1937), The Free Wind operetta (1947), and music to the films Circus (1935) and The Kuban Cossacks (1949).
He died of a heart attack in Moscow in 1955. His last piece, the operetta White Acacia (1955), was left unfinished at his death. It was completed by Kirill Molchanov and staged on 15 November 1955, in Moscow.