Leo Smit was born to Russian immigrants on January 12, 1921, in Philadelphia. He received his earliest musical training from his father, Kolman Smit, beginning at age five. Kolman Smit was a professional violinist who performed in the Philadelphia Orchestra (1926-1931) under Leopold Stokowski, the Cincinnati Symphony under Fritz Reiner, and the NBC Symphony under Arturo Toscanini.

After private piano studies with Martha Lantner, Joseph Wissof, and Bert Shefter, Smit traveled to Moscow with his mother in 1929 to study piano for three months with Dmitri Kabalevsky on scholarship at the Moscow Conservatory. Upon his return to Philadelphia, Smit received a scholarship in 1930 to study piano at Curtis Institute of Music with noted piano pedagogue Isabelle Vengerova. He continued his studies on scholarship in New York, studying piano with José Iturbi (1933-35) and composition with Nicolas Nabokov (1935). It was under Nabokov's tutelage that Smit produced his first original composition in 1935, Zvay, a song setting of a Yiddish poem by Mani Loeb for soprano and piano.

Smit began his professional career as a pianist while still in his teens. His first professional engagement was as rehearsal pianist for George Balanchine's American Ballet Company in 1936-37. A year after beginning in this position, Smit met Igor Stravinsky during rehearsals of the composer's ballet, Jeu de Cartes. Smit gave his debut recital as a solo pianist at Carnegie Hall in February 1939. His successful debut was followed by a concert tour of the United States in 1940.

Leo Smit's career as composer, pianist, conductor, and educator spanned seven decades of musical life in the United States. He established close working relationships, and/or friendships, with many of the most prominent musicians of the 20th century, including Igor Stravinsky, Béla Bartók, Aaron Copland, Leonard Bernstein, Harold Shapero, William Schuman, Alex Haieff, Leopold Stokowski, and Lukas Foss. As a performer, Smit was an enthusiastic and persuasive advocate and interpreter of the music of his time, especially the solo piano music of Aaron Copland. His compositional output totals more than one hundred works, including two operas, three symphonies, more than ninety songs, two ballets, and numerous chamber and piano works.

Smit was also a talented photographer. In addition to the many photographs he took of noted musicians, Smit also used his skill as a photographer to capture images from his travels. Many of his travel pictures reflect his reverence for nature. As part of his innovative approach to programming, Smit would often include displays of his photography in his theme-based concerts.

During his career Leo Smit earned several awards and honors, including Fulbright (piano) and Guggenheim (composition) Fellowships in 1950, a fellowship at the American Academy in Rome for 1950-51, the Boston Symphony Merit Award in 1953 for his Symphony No. 1 (premiered October 16, 1953 by the Boston Symphony Orchestra, conducted by Charles Munch), the New York Critics Circle Award in 1957 (also for his Symphony No. 1), his selection as an artist for a State Department concert tour of Latin America in 1967-68, and the Buffalo Evening News Man of the Year award in 1969. As an educator, Smit held positions at Sarah Lawrence College (1947-49), UCLA (1957-63), and the State University of New York at Buffalo (1962-84).

Leo Smit died December 12, 1999 in Scripps Hospital, Encinitas, California.