Heath-Stubbs was born in London in 1918, and educated Queen's College, Oxford. He co-edited Eight Oxford Poets in 1941, with Sidney Keyes and Michael Meyer, and helped edit Oxford Poetry in 1942–43. He held the Gregory Fellowship of Poetry at Leeds University (1952-55) and he had professorships in Alexandria (1955-58) and Ann Arbor, Michigan (1960-61). He taught at the College of St Mark and St John in Chelsea (1962-72), as well as at Merton College, Oxford for twenty years from 1972. He translated, among others, Sappho, Horace, Catullus, Hafiz, Verlaine, and most notably Giacomo Leopardi.
He was a representative figure of British poetry in the early 1950s, editing the poetry anthology Images of Tomorrow (1953) and, with David Wright, the Faber Book of Twentieth Century Verse, among others. He was elected to the RSL in 1954, awarded the Queen's Gold Medal for Poetry 1973, and appointed OBE in 1989. Although afflicted by blindness from the 1960s, and completely without sight from 1978, he continued to write almost to the end. He died on Boxing Day 2006.