Born in Johannesburg in South Africa, Cormack was educated at the University of Cape Town. He became interested in x-ray imaging at the Groote Schuur Hospital in Johannesburg, where he worked as a physicist in the radioisotopes department. In 1956 he moved to America where he served as professor at Tufts University, Massachusetts, until his retirement in 1994.

Cormack was the first to analyze theoretically the possibilities of developing a radiological cross-section of a biological system. Independently of the British engineer Godfrey Hounsfield, he developed the mathematical basis for the technique of computer-assisted x-ray tomography (CAT), describing this in two papers in 1963 and 1964, and provided the first practical demonstration. X-ray tomography is a process by which a picture of an imaginary slice through an object (or the human body) is built up from information from detectors rotating around the body. The application of this technique to medical x-ray imaging was to lead to diagnostic machines that could provide very accurate pictures of tissue distribution in the human brain and body. Hounsfield was unaware of the work of Cormack when he developed the first commercially successful CAT scanners for EMI in England.

Cormack also pointed out that the reconstruction technique might equally be applied to proton tomography, or to gamma radiation from positron annihilations within a patient, and he investigated these as possible imaging techniques.

Cormack shared the 1979 Nobel Prize for physiology or medicine with Hounsfield for the development of CAT.