Peters grew up in Merthyr Tydfil and studied Geography and History at University College of Wales, Aberystwyth, graduating immediately before the Second World War.
He served in the Royal Air Force from 1939 to 1945, primarily in photographic reconnaissance in the Middle East and the Mediterranean.
Before completing his doctorate at the University of Oxford in 1951 he also studied Classical Arabic there.
After graduating he briefly taught at Cambridge, and in 1952 was appointed Lecturer in Social Anthropology at the University of Manchester, becoming a full professor in 1968.
The Department of Social Anthropology of the University of Manchester awards an Emrys Peters Essay Prize in his memory, from a gift made by his widow Stella.