Son of Archibald Stuart (1691-1767) and Elizabeth Myreton (ca. 1700-1772). Brother-in-law of Boswell's grand-uncle, Thomas Cochrane, who was married to Stuart's sister Jane (1722-1808).
As a Scottish Writer to the Signet (solicitor), Stuart served as tutor and guardian of the children of James, 6th Duke of Hamilton, and even represented the family in the Douglas Cause against A.J.E. Douglas. Appointed member of the signet of Scotland in 1770, and later a Member of Parliament (1774-1784 for Lanarkshire, and 1790-1801). Sometime Commissioner on the Board of Trade.
In 1773 Stuart published Letters to the Right Honourable Lord Mansfield, an attack upon Lord Mansfield for his conduct in the Douglas cause. In 1798 he published A Genealogical History of the Stewarts, which was, apparently, knowingly faulty due to Stuart's wish to prove that the Stewarts of Castlemilk - of which he became the senior member in 1797 - was the senior legitimate branch of the Stewart family.
Stuart was an early member of The Poker Club, and a close friend of philosopher Adam Smith. He was also an acquaintance of French philosopher Helvetius (1715-1771), who refers to him in a few of his letters.1
- 1Cumming, Ian. (1955). Helvetius: his life and place in the history of educational thought. p. 100
Boswell met Stuart, whom he had not seen for two years, in The Hague on June 1, 1764, together with William Nairne. Stuart was then on a fact-finding mission in connection with the Douglas Cause, and Boswell spent most of the day in their company, together with a Colonel Scott, going with them (in a coach) to Delft and Rotterdam. Stuart promised Boswell to get Basil Cochrane to convince Boswell's father to allow Boswell "a pretty handsome tour abroad". Basil Cochrane was Boswell's grand-uncle, and the brother of Stuart's brother-in-law, Thomas Cochrane.