Denys Page was born in Reading on 11 May 1908 to Elsie, née Daniels, and Frederick Page, a chartered civil engineer for the Great Western Railway, and was one of five children. After education at Newbury grammar school he won a scholarship to Christ Church, Oxford in 1926, where he benefitted most from the teaching of Gilbert Murray, J. D. Beazley, and J. D. Denniston. In 1928 Page was Craven and De Paravicini scholar, and won the Chancellor's prize for Latin verse and the Gaisford prize for Greek verse. He obtained first classes in both Mods (1928) and Greats (1930), and was then elected to the Derby scholarship and spent a year at the University of Vienna studying with Ludwig Radermacher.
In 1931 he was appointed a lecturer at Christ Church, and tutor the following year. His university life was interrupted by the Second World War: in 1939 he was recruited to the Government Code and Cypher School at Bletchley Park; he worked in the ISOS 'illicit signals' section under Oliver Strachey, and succeeded him as head of the section in 1942. After the war, he headed a special command mission to Viscount Mountbatten's headquarters in Sri Lanka and then Singapore, not returning to Oxford until 1946.
Page served as Senior Proctor in 1948-1949, but in 1950 he was offered the position of Regius Professor of Greek at Cambridge on the retirement of D. S. Robertson, though he had not applied for the post, and accepted it. He was elected to a professorial fellowship at Trinity, though in 1959 he was chosen as master of Jesus College, a position he held until his retirement in 1973. Page was elected a fellow of the British Academy in 1952, and was awarded its Kenyon Medal in 1969; he served as president of the Academy from 1971-1974. He was knighted in 1971.
His greatest scholarly achievements were as an editor of Greek texts, particularly the Greek lyric poets; he also worked on Hellenistic poetry, producing an edition of the epigrams of the Greek Anthology with his Trinity colleague A. S. F. Gow, tragedy, and the Homeric poems.
In 1939 Page married Katharine Elizabeth Dohan (1918-1978), daughter of archaeologist Edith Hayward Hall Dohan (1877-1943) and Joseph M. Dohan, a lawyer and farmer; they had four daughters.