He was born at Boston in Lincolnshire, and is said to have learned the alphabet at fourteen months, and to have been reading well at three and a half. He was educated at Beverley Grammar School, at Rugby School and at Oxford, where, after matriculating at University College, he came into residence at Magdalen, where he had been nominated to a demyship. He was Ireland and Hertford scholar in 1844; in March 1846 he was elected to a scholarship at University College, and in December of the same year he obtained a first class in classics; in February 1848 he became a fellow of University. He also obtained the Chancellor's prize for Latin verse (1847), English essay (1848) and Latin essay (1849). He successfully applied for the Eldon law scholarship in 1849, and went to Lincoln's Inn; but after six months he resigned the scholarship and returned to Oxford.
During his brief residence in London he began writing for the Morning Chronicle, and continued to do so after leaving. He showed no special aptitude for journalism, but a series of articles on university reform (1849–1850) was the first public expression of his views on a subject that always interested him. In 1854 his appointment, as first occupant, to the chair of Latin literature, founded by Corpus Christi College, Oxford, gave him a congenial position. From this time he confined himself with characteristic conscientiousness almost exclusively to Latin literature. The only important exception was the translation of the last twelve books of the Iliad in the Spenserianstanza in completion of the work of P.S. Worsley, and this was undertaken in fulfilment of a promise made to his dying friend. In 1852 he began, in conjunction with Prof. Goldwin Smith, a complete edition of Virgil with a commentary, of which the first volume appeared in 1858, the second in 1864, and the third soon after his death. Goldwin Smith was compelled to withdraw from the work at an early stage, and in the last volume his place was taken by Henry Nettleship.
In 1866 Conington published his most famous work, the translation of the Aeneid of Virgil into the octosyllabic metre of Sir Walter Scott. John Dryden's version is the work of a stronger artist; but Conington's is more faithful, preserves the general effect of the original, and stands as an independent poem. That the measure chosen does not reproduce the majestic sweep of the Virgilian verse is a fault in the conception and not in the execution.