Tworkov immigrated to the United States in 1913. After receiving a degree in creative writing from Columbia University (1923), he returned to his earlier interest in painting.

Tworkov's early paintings reflect his profound admiration for the work of Paul Cézanne. While working for the WPA federal arts project in 1935, however, he met the painter Willem de Kooning (de Kooning, Willem), and Tworkov subsequently abandoned his figurative style. After World War II he joined de Kooning and other artists, who together evolved Abstract Expressionism (q.v.).

By 1955 Tworkov revealed his mature style in works that are built up of countless diagonal strokes of paint, creating shimmering atmospheric fields of colour. Later he replaced the multitude of flickering lines with broad strokes; these forceful compositions culminated in the gridlike format of such paintings as “Variables” (1963). In the late 1960s the grid work became literal in the “Crossfield” series (begun 1968); in these, Tworkov superimposed a network of ruled lines onto an overall field of widely spaced strokes “drawn” in paint.

From 1963 to 1969 he was chairman of the department of art at Yale University.