Dodds was born in Banbridge, County Down, the son of schoolteachers. His father Robert was from a Presbyterian family, and died of alcoholism when Dodds was seven. His mother Anne was of Anglo-Irish ancestry. When Dodds was ten, he moved with his mother to Dublin, and he was educated at St Andrew's College (where his mother taught) and at Campbell College in Belfast. He was expelled from the latter for "gross, studied and sustained insolence".
In 1912, Dodds won a scholarship at University College, Oxford to read classics, or Literae Humaniores (a two-part four-year degree program consisting of five terms' study of Latin and Greek texts followed by seven terms' study of ancient history and ancient philosophy). Friends at Oxford included Aldous Huxley and T. S. Eliot. In 1916, he was asked to leave Oxford due to his support for the Easter Rising, but he returned the following year to take his final examinations in Literae Humaniores, and was awarded a first class degree to match the first-class awarded him in 1914 in Honour Moderations, the preliminary stage of his degree. His first tutor at Oxford was A. B. Poynton.
After graduation, Dodds returned to Dublin and met W. B. Yeats and AE (George William Russell). He taught briefly at Kilkenny College and in 1919 was appointed as a lecturer in classics at the University of Reading, where in 1923 he married a lecturer in English, Annie Edwards Powell (1886–1973). They had no children.
In 1924, Dodds was appointed Professor of Greek at the University of Birmingham, and came to know W. H. Auden (whose father George, Professor of Public Medicine and an amateur classicist, was a colleague). Dodds was also responsible for Louis MacNeice's appointment as a lecturer at Birmingham in 1930. He assisted MacNeice with his translation of Aeschylus, Agamemnon (1936), and later became the poet's literary executor. Dodds published one volume of his own poems, Thirty-Two Poems, with a Note on Unprofessional Poetry (1929).
On 22 December 1926 E. R Dodds witnessed a spectacular 'first'. He was the son-in-law of pioneer aviator Canon Powell of Watermillock, and was visiting him for Christmas in the Lake District. He had heard of the attempt to land an aircraft on Helvellyn earlier that month, but the flyers John F. Leeming and Bert Hinkler had been delayed by weather and mechanic problems. The earlier attempts would have been recorded by Mr. Sandham, the manager of Thirlmere reservoir, who made a previous reconnaissance visit with Leeming to clear a landing strip. He decided on another attempt, but unfortunately by this time Sandham had retired from the mountain. After an eventful bumpy flight over the Lake District they spiralled down to the summit. No doubt looking for the cleared strip. Leeming also noticed someone sheltering at the summit cairn. A witness (E.R. Dodds). The landing was easy as strong headwind and steep slope stopped them at once. Once down Hinckler had to use full throttle on the slope, whilst Leeming found rocks to chock the wheels to stop them rolling backwards. Luckily the witness Dodds had gone up half expecting the aviators to try again. Not one of them had brought a pencil and paper to record the event. After much searching a scrap of paper and pencil stub was found in a jacket pocket. Dodds signed resting on the wing. Photographs taken. A letter in a tin box was left for Sandham which still exists today in a relative's house in Penrith.
In 1936, Dodds became Regius Professor of Greek at the University of Oxford, succeeding Gilbert Murray. Murray had decisively recommended Dodds to Prime Minister Stanley Baldwin (the Chair was in the gift of the Crown) and it was not a popular appointment – he was chosen over two prominent Oxford dons (Maurice Bowra of Wadham College and John Dewar Denniston of Hertford College). His lack of service in the First World War (he had worked briefly in an army hospital in Serbia but later invoked the exemption from military service granted Irish residents) and his support for Irish republicanism and socialism in addition to his scholarship on the non-standard field of Neoplatonism, also did not make him initially popular with colleagues. He was treated particularly harshly by Denys Page at whose college (Christ Church) the Regius Chair of Greek was based. Oxford rumor has it that Maurice Bowra could not live down the disappointment of not being named Regius Professor and instigated behind-the-scene opposition and underhanded behavior by his circle of classical dons to make Dodds' initial months as professor difficult.
Dodds had a lifelong interest in mysticism and psychic research, being a member of the council of the Society for Psychical Research from 1927 and its president from 1961 to 1963.
He died in Old Marston, northeast of Oxford.
Among his works are The Greeks and the Irrational (1951), which charts the influence of irrational forces in Greek culture up to the time of Plato, and Pagan and Christian in an Age of Anxiety, a study of religious life in the period between Marcus Aurelius and Constantine I.
For a bibliography of Dodds' publications see Quaderni di Storia no. 48 (1998) 175-94 (with addenda in the same journal, no. 61, 2005), and for general information on him and studies of some of his works see the bibliography to the entry for him in The Dictionary of British Classicists (2004), vol. 1, 247–51. Add the articles on his work on Neoplatonism in Dionysius 23 (2005) 139-60 and Harvard Studies in Classical Philology 103 (2007) 499–542.
He was also editor of three major classical texts for the Clarendon Press, Proclus: Elements of Theology, Euripides' Bacchae and Plato's Gorgias, all published with extensive commentaries, and a translation in the case of the first. His autobiography, Missing Persons, was published in 1977.
He edited Louis MacNeice's unfinished autobiography The Strings are False (1965) and MacNeice's Collected Poems (1966).Thirty-Two Poems: With a Note On Unprofessional Poetry (1929)
Why I Do Not Believe in Survival (1934)
Humanism and Technique in Greek Studies (1936)
Maenadism in the Bacchae (1940)
Minds in the Making (1941)
The Greeks and the Irrational (1951)
Morals and Politics in the Oresteia (1960)
Classical Teaching in an Altered Climate (1964)
Pagan and Christian in an Age of Anxiety (1965)
Supernormal Phenomena in Classical Antiquity (1971)
The Ancient Concept of Progress and Other Essays on Greek Literature and Belief (1973)
Missing Persons: An Autobiography (1977)