Thompson was born in Devlin, Ontario, Canada, and studied at the University of British Columbia, where he received his B.A. (1925) and M.A. (1927) in classics. In 1929 he received his Ph.D. from the University of Michigan; at Michigan it was Benjamin Dean Meritt (later a faculty member at the Institute for Advanced Study) who introduced Thompson to the project which would occupy him for the rest of his life. The American School of Classical Studies at Athens was about to begin the excavation of the agora in Athens and Thompson was selected as a fellow of the school to aid in the project. Excavations began on May 25, 1931; Thompson would work on the excavations for the next 39 years. He was married to the archaeologist Dorothy Burr Thompson.
Thompson was Professor Emeritus at the Institute for Advanced Study, where he had joined the faculty in 1947.
Thompson received numerous awards during his long career. These included: the Gold Medal for Distinguished Archaeological Achievement from the Archaeological Institute of America (1972), the Lucy Wharton Drexel Gold Medal of the University Museum at the University of Pennsylvania (1978), the Kenyon Medal for Classical Studies from the British Academy (1991), and the Thomas Jefferson Medal for Distinguished Achievement in the Humanities from the American Philosophical Society (1996).
Thompson died in Hightstown, New Jersey.