Educated at the Edinburgh Academy and afterwards at the University of Glasgow, he entered Balliol College, Oxford, as a scholar. Graduating with a first-class in classics, he was elected fellow of Oriel, and, after holding assistant professorships at Durham, Glasgow and St Andrews, was appointed professor of Greek at St Andrews (1857). In 1863 he was elected professor of humanity in Edinburgh University, and occupied that chair till his death.
Sellar was one of the most brilliant of modern classical scholars, and was remarkably successful in his endeavours to reproduce the spirit rather than the letter of Roman literature.
His chief works are: The Roman Poets of the Republic (3rd ed., 1889) and The Roman Poets of the Augustan Age (Virgil, 3rd ed., 1897), and Thrace and the Elegiac Poets (2nd ed., by WP Ker, 1899), with memoir by Andrew Lang, are standard authorities.