Koussevitzky studied music in Moscow. He was initially a virtuoso double bass player (he wrote a concerto for the instrument in 1905), with his conducting debut coming in 1908 in Berlin. The following year he founded his own orchestra. He left the Soviet Union in 1920 and stayed in Paris before moving to the United States in 1924 (he became a US citizen in 1941). From 1924 to 1949 he was conductor of the Boston Symphony Orchestra, developing its summer concert programme at Tanglewood.
Koussevitzky was a great champion of modern music, commissioning a number of works from prominent composers, including Igor Stravinsky's Symphony of Psalms (commissioned to celebrate the fiftieth anniversary of the Boston Symphony). In 1942 he founded the Koussevitzky Foundation to commission and perform new works - among the results were Benjamin Britten's opera Peter Grimes and Béla Bartók's Concerto for Orchestra.