He attended high school at Western Reserve Academy, a private, coeducational boarding school in Hudson, Ohio. He then went to Yale University, where he obtained an B.A. (1934), M.A. (1936) and Ph.D. degree (1940), the latter two under guidance of Henri Focillon.
From 1938 onwards, Kubler was a member of the Yale University faculty and was the first Robert Lehman Professor (1964-1975), Sterling Professor of the History of Art (1975-1983). He was appointed the 1985-1986 Kress Professor at the Center for Advanced Studies at the National Gallery of Art in Washington, D.C. After his retirement, He was a senior resident scholar of the Yale University.
Kubler contributed articles to art journals and to several anthologies, including the Smithsonian’s "Handbook of South American Indians".
He died on October 3, 1996, in Hamden, Connecticut, United States.
He married Elizabeth Bushnell in 1937. They had 4 children: Alexandra, Cornelia, Edward, Elena.