He was the son of composer Meliton Balanchivadze and brother of ballet choreographer George Balanchine.
Born in Saint Petersburg, Russian Empire, he graduated from the Tbilisi State Conservatoire in 1927 and Leningrad Conservatory in 1931, where he studied with Pyotr Ryazanov.
Having barely survived Joseph Stalin's purges, he became a professor at the Tbilisi Conservatory in 1942 and served as an artistic director of the Georgian State Symphony from 1941 to 1948.
He became a major influence in musical politics as chair (1953), and first secretary (1955–1961, 1968–1972) of the Union of Georgian Composers.
Balanchivadze’s numerous symphonies, pianoforte concertos, and compositions for the stage heavily contributed to modern Georgian classical music.