Steinberg was born in Romania where he was to study philosophy for a year at the University of Bucharest, later enrolling at the Politecnico di Milano, studying architecture, graduating in 1940. During his years in Milan he was actively involved in the satirical magazine Bertoldo.

Steinberg left Italy after the introduction of anti-Semitic laws by the Fascist government. He spent a year in the Dominican Republic awaiting a U.S. visa; in the meantime, he submitted his cartoons to foreign publications. In 1940, he was given commissions from magazines and newspapers and sold cartoons to Harper’s Bazaar and Life. In 1942, The New Yorker magazine, having published his first cartoon in 1941, sponsored his entry into the United States-- thus began Steinberg's lifelong relationship with the publication. Through well over half a century working with The New Yorker, Steinberg created 87 covers, 33 cartoons and 71 portfolios containing 469 drawings and several hundred other works amounting to more than 1,200 drawings.

Steinberg exhibited throughout his career at art museums and galleries. In 1946, Steinberg, along with artists such as Arshile Gorky, Isamu Noguchi, and Robert Motherwell, was exhibited in the critically acclaimed "Fourteen Americans" show at MOMA, as well as in a retrospective at the Whitney Museum of American Art (1978) and a posthumous show at the Institute for Modern Art in Valencia (IVAM), Spain (2002).