He was born in Moscow and studied conducting at the conservatory there. From 1955 he conducted at the Bolshoi Theatre, being appointed principal conductor there in 1962. From 1965 he was principal conductor of the USSR State Symphony Orchestra (now the Russian State Symphony Orchestra). In 1979 he was appointed principal guest conductor of the London Symphony Orchestra.
Svetlanov was particularly noted for his interpretations of Russian works - he covered the whole range of Russian music, from Mikhail Glinka to the present day.