Dunayevsky was born to a Jewish family in Lokhvitsa, Poltava Governorate, Russian Empire in 1900. He studied at the Kharkiv Musical School in 1910 where he studied violin under Joseph Achron. During this period he started to study the theory of music under Semyon Bogatyrev (1890 – 1960). He graduated in 1919 from the Kharkiv Conservatory. At first he was a violinist, the leader of the orchestra in Kharkiv. Then he started a conducting career. In 1924 he went to Moscow to run the Theatre Hermitage. After that he worked in Leningrad (1929 – 1941) as a director and conductor of the "Music - Hall" (1929 – 34) and then moved to Moscow to work on his 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.

A previously unknown opera libretto Rachel (1943) by Mikhail Bulgakov, was later found in his archive. The libretto was based on Guy de Maupassant's Mademoiselle Fifi and was published in a book by Naum Shafer.

A book of his essays and memoirs was published in 1961.

Dunayevsky was named a People's Artist of Russia in 1950. He was twice awarded the Stalin Prize (1941, 1951) and received two orders and many medals (including the Order of the Red Labour Banner, the Order of the Red Star, and the Badge of Honour).

His brother Semyon (1906 – 1986) was a conductor; another brother, Zinovy (1908 – 1981), was a composer.

Dunayevsky was married twice. He had a son Yevgeny (b. 1932) by his wife Zinaida Sudeikina, and another son Maksim (b. 1945) by his lover, the ballerina Zoya Pashkova. Maksim was also a well known composer, and continues the traditions of his father in musicals and operettas.