Born in London, he was the son of Edward Edwards (1870–1944) of the British Museum, and his wife Ellen Jane Higgs. He attended Merchant Taylors' School, where he studied Hebrew, and then Gonville and Caius College, Cambridge, gaining a first class in Oriental Languages. He was awarded the William Wright studentship in Arabic and received his doctorate in 1933.
In 1934 Edwards joined the British Museum as Assistant Keeper in the Department of Egyptian and Assyrian Antiquities. He published Hieroglyphic Texts for Egyptian Stellae. in 1939. During World War II he was sent to Egypt on military duty. In 1946 he wrote The Pyramids of Egypt, which was published by Penguin Books in 1947. In 1955 he was appointed the Keeper of Egyptian Antiquities at the British Museum and organized the Tutankhamun exhibition in 1972. He remained there until his retirement in 1974.
On leaving the British Museum he worked with UNESCO during the rescue of the temple complex at Philae. He was also Vice-President of the Egypt Exploration Society, a Fellow of the British Academy (1962) and was awarded the CBE in 1968 for his services to the British Museum.