Fagles was born in Philadelphia, Pennsylvania, the son of Charles Fagles, a lawyer, and Vera Voynow Fagles, an architect. He attended Amherst College, graduating in 1955 with a Bachelor of Arts degree. The following year, he received his master's degree from Yale University. On June 17, 1956, he married Lynne Duchovnay, a teacher, and they had two children. In 1959, Fagles received his Ph.D in English from Yale and for the next year taught English there.

From 1960 to 1962, Fagles was an English instructor at Princeton University. In 1962 he was promoted to Assistant Professor, and in 1965 became an Associate Professor of English and comparative literature. Later that year he became director of the comparative literature program. In 1970, he became a full professor, and from 1975 was the department chair. He retired from teaching as the Arthur W. Marks '19 Professor of Comparative Literaure in 2002, and remained a professor emeritus at Princeton.

Between 1961 and 1996, Fagles translated many ancient Greek works. His first translation was of the poetry of Bacchylides, publishing a complete set in 1961. In the 1970s, Fagles began translating much Greek drama, beginning with Aeschylus'sThe Oresteia. He went on to publish translations of Sophocles's three Theban plays (1982) and Homer's Iliad (1990) and Odyssey (1996). In all of the last three, Bernard Knox authored the introduction and notes. Fagles' translations generally emphasize contemporary English phrasing and idiom but are faithful to the original ancient Greek as much as possible.

In 1978, Fagles published I, Vincent: Poems from the Pictures of Van Gogh. He was the co-editor of Homer: A Collection of Critical Essays (1962) and Pope's Iliad and Odyssey (1967).

Fagles died at his home in Princeton, New Jersey on March 26, 2008, from prostate cancer.