Born to Jewish parents in St. Petersburg, Russia, Bolotowsky immigrated to America in 1923 via Constantinople, settling in New York City. He attended the National Academy of Design. He became associated with a group called "The Ten Whitney Dissenters," or simply "The Ten," artists, including Louis Schanker, Adolph Gottlieb, Mark Rothko and Joseph, who rebelled against the strictures of the Academy and held independent exhibitions.

During this period, Bolotowsky came under the influence of the Dutch painter Piet Mondrian and the tenets of neoplasticism, a movement that advocated the possibility of ideal order in the visual arts. Bolotowsky adopted his mentor's use of horizontal and vertical geometric pattern and a palette restricted to primary colors and neutrals.

In 1936, having turned to geometric abstractions, he was one of the founding members of the American Abstract Artists, a cooperative formed to promote the interests of abstract painters and to increase understanding between themselves and the public.