Son of James Stewart (d. 1746), 5th Earl of Galloway, and Catherine Montgomerie (d. 1757), daughter of the 9th Earl of Eglinton. Married (1719) to Anne Keith (d. 1728), daughter of William Keith, 9th Earl Marischal. Married (1729) to Catherine Cochrane, daughter of John Cochrane, 4th Earl of Dundonald. Father of at least 10 children, among them John, Keith, Harriet and Catherine Stewart. He died at Aix-en-Provence on September 24, 1773.
6th Earl of Galloway (1746-1773). Lord Garlies (-1746). Lord of Police (1743-1768), Grand Master of the Grand Lodge of Scotland (1757-1759), President of the Council of the Royal Archers (1765-1768).
Boswell visited Lord Galloway on his Harvest Jaunt in 1762, arriving at Galloway House on September 25. He described the Lord as "a man of great quickness and uncommon spirits for his age. He has seen a great deal and has lived always as a man of pleasure, that is to say, he has followed his own inclinations. Politics is the great study of his life, which have led him to do things not at all right. He is a good father, a good husband, a good master. Had he never engaged in politics he might have passed through life with esteem, without any disagreeable imputation."