Cooper, who was born in New York City, was educated at Columbia where he obtained his PhD in 1954. After brief spells at the Institute for Advanced Study, Princeton, the University of Illinois, and Ohio State University, he moved in 1958 to Brown University, Providence, and was later (1962) appointed to a professorship of physics.

Cooper's early work was in nuclear physics. In 1955 he began work with John Bardeen and John Robert Schrieffer on the theory of superconductivity. In 1956 he showed theoretically that at low temperatures electrons in a conductor could act in bound pairs (now called Cooper pairs). Bardeen, Cooper, and Schrieffer showed that such pairs act together with the result that there is no electrical resistance to flow of electrons through the solid. The resulting BCS theory stimulated further theoretical and experimental work on superconductivity and won its three authors the 1972 Nobel Prize for physics.

Cooper has also worked on the superfluid state at low temperatures and, in a different field, on the theory of the central nervous system.