Bolotowsky was born in the Russian city of Saint Petersburg. After the Russian Revolution, his family moved to Istanbul in 1921, then to New York in 1923; Bolotowsky became an American citizen in 1929. In New York, he studied at the National Academy of Design and developed an interest in the biomorphic forms of Surrealist art, as well as geometric abstraction. The Neoplastic style of abstraction defined by Piet Mondrian would prove to be the greatest influence on Bolotowsky's work. Mondrian practiced a form of purely nonrepresentational art, in which compositions of right angles and primary colors held no associations with the natural world.
Bolotowsky began producing his own strictly abstract art in the early 1930s, and his admiration for Mondrian's approach is evident even in such late works as Large Blue Horizontal. The orderly, grid-based composition of this painting is marked by black and white lines of various widths and rectangular areas of unmodulated primary colors. Like Mondrian, Bolotowsky strove to establish a balance of horizontals and verticals that would be at once harmonious and dynamic.
Bolotowsky was a constant advocate of abstract art, speaking to a wider audience through exhibitions, publications, and lectures. He was a founding member of American Abstract Artists, which eventually included American artists such as Burgoyne Diller and Willem de Kooning, and European artists living in the United States, among them Fernand Léger, Joseph Albers, Jean Hélion, and Mondrian himself. He was also a member of "The Ten", an artists' group that included Mark Rothko and Adolph Gottlieb, and during the Great Depression of the 1930s he worked for the Works Progress Administration / Fine Arts Project, painting a number of abstract murals for public buildings in New York. In 1946, Bolotowsky was appointed head of the art department at Black Mountain College, the first of many teaching positions he would hold throughout his career.