He studied at the School of Industrial Arts (now the University of the Arts (Philadelphia) in 1937, the Pennsylvania Academy of Art in 1938, at the Barnes Foundation in 1941 where he had a scholarship and from 1951-54 at the California School of Fine Art (now the San Francisco Art Institute).
Primarily a painter, Kelly also created graphic work especially during his early years in San Francisco from 1950 to 1953. He interrupted his art career by enlisting in the Air Force in World War II, serving in the Pacific repairing the ultra-secret Norden bombsight for Boeing B-24 planes for the entirety of the war. It was there that he produced several significant lithographic works.
One of them, "Deep Blue I" from 1952, is considered a masterpiece by Charles Dean, whose Abstract Expressionist collection was acquired by the Library of Congress. Kelly has been categorized as a "second-generation" abstract expressionist. In 1953 Kelly married painter Sonia Gechtoff.
The couple became fixtures in the roiling art community of the day. He supplemented his artist's income with jobs as a preparator at the San Francisco Museum of Art and as a bartender at The Place. Kelly and Gechtoff moved to New York in 1958.
He worked at Grove Press for several years, leaving to concentrate on his painting which continued uninterrupted for the rest of his career. King Ubu Gallery, San Francisco, 1953 San Francisco Museum of Art, 1957, 1958, 1965 Ferus Gallery, Los Angeles, 1958, 1959 "California Painting and Sculpture: The Modern Era", Smithsonian Institution, 1977 "The San Francisco School of Abstract Expressionism", San Francisco Museum of Modern Art, 1996.
Served with United States Air Force, 1941-1945. Member National Academy of Design.
Married Sonia Gechtoff, June 23, 1953. Children– Susannah, Miles.