John Alexander Stewart was born at Moffat, Dumfriesshire on 19 October 1846, the son of Archibald Stewart. Educated at Edinburgh University and Lincoln College, Oxford, he received the Newdigate Prize for English verse in 1868; he recited the prize-winning poem, 'The Catacombs', in the Theatre, Oxford, on 17 June that year. Stewart earned a BA in 1870 and an MA three years later. He was also elected Senior Student of Christ Church, a position he held from 1870 to 1875, prior to marrying Helen J. Macmillan. Following his graduation, he continued to teach at Christ Church and was a classical lecturer there until 1882,, occasional tutor and philosophy lecturer until 1897.

Over the next decade, he gradually established a formidable reputation as an authority on the ethics of Aristotle. Among his works were the 2-volume Nicomachean Ethics of Aristotle (1892) and The Myths of Plato (1905). He was also a contributor to the Encyclopædia Britannica. In 1897, he was appointed White's professor of moral philosophy at Oxford and Fellow of Corpus Christi College. His wife Helen died in 1925 and Stewart resigned his position at the college two years later. Stewart died at Oxford on 27 December 1933.