Black graduated from St. Andrews University in 1946 and, after a number of academic posts, joined ICI as a pharmacologist (1958–64). After working with Smith, Kline and French he became professor of pharmacology at University College, London (1973–77), before joining Wellcome as Director of Therapeutic Research (1978–84). From 1984 he was professor of analytical pharmacology at King's College Hospital, London.

Black has been associated with two important advances in pharmacology. In the 1950s he isolated the first beta blockers. These are compounds that prevent the stimulation of certain nerve endings (beta receptors) in the sympathetic nervous system, thus reducing heart activity. Beta blockers are widely used to treat hypertension and angina. His subsequent work was concerned with the control of gastric ulcers and his discovery of the drug cimetidine, which reduces acid secretion in the stomach and is used to treat ulcers in the stomach and duodenum. For this work and his earlier work on beta blockers he was awarded the 1988 Nobel Prize for physiology or medicine.