Soulima was the son of Igor Stravinsky and the grandson of Fyodor Stravinsky. He studied piano with Isadore Philipp and also theory and composition with Nadia Boulanger. In addition to his many musical compositions, he wrote books on orchestration and the orchestra. His book on Orchestration contains an excellent section on Brass instruments including many unusual instruments.
In 1950, Soulima Stravinsky was appointed to the School of Music of the University of Illinois, USA, to the piano faculty. While continuing his concerto solo career, he also began to distinguish himself as a composer, transcriber and editor. He was awarded the “Chevalier des Arts et des Lettres” by the French Ministry of Cultural Affairs in 1974.