The son of an Englishwoman and a Lebanese businessman trading in Brazil, Medawar was born in Rio de Janeiro and brought to Britain at the end of World War I. He was educated at Oxford, graduating in zoology in 1937, and remained there to work under Howard Florey. His first researches concerned factors affecting tissue-culture growth but during World War II he turned his attention to medical biology. He subsequently developed a concentrated solution of the blood-clotting protein fibrinogen, which could be used clinically as a biological glue to fix together damaged nerves and keep nerve grafts in position.

The terrible burns of many war casualties led Medawar to study the reasons why skin grafts from donors are rejected. He realized that each individual develops his own immunological system and that the length of time a graft lasts depends on how closely related the recipient and donor are. He found that grafting was successful not only between identical twins but also between nonidentical, or fraternal, twins. It had already been shown in cattle that tissues, notably the red-cell precursors, are exchanged between twin fetuses. This led to the suggestion by Macfarlane Burnet that the immunological system is not developed at conception but is gradually acquired. Thus if an embryo is injected with the tissues of a future donor, the animal after birth should be tolerant to any grafts from that donor.

Medawar tested this hypothesis by injecting mouse embryos, verifying that they do not have the ability to form antibodies against foreign tissue but do acquire immunologic tolerance to it. For this discovery Medawar and Burnet were awarded the 1960 Nobel Prize for physiology or medicine.

Medawar moved from Oxford in 1947 to the chair of zoology at Birmingham, a post he held until 1951 when he was appointed professor of zoology at University College, London. In 1962 he accepted the important post of director of the National Institute for Medical Research. For some years he tried to combine his research work with a heavy administrative load. But in 1969 Medawar suffered his first stroke. Although he continued as director until 1971, the stroke had seriously restricted his mobility and dexterity. Despite this he continued his research work on cancer at the Clinical Research Centre, London. A second stroke in 1980, and a third in 1984, brought Medawar's research career to an end.

He continued to write, however, and in 1986 published his autobiography, Memoirs of a Thinking Radish, and collected most of his early essays in Pluto's Republic (1982). It was in one of these essays, first published in 1964, that Medawar characterized science in a much quoted phrase as “the art of the soluble.”