Son of William Veitch of Eliock (d. 1747), a Writer to the Signet. Sometime Sheriff Depute of Peebles. Sometime MP for Dumfries. Appointed Lord of Session as Lord Eliock in 1761. He was unmarried.
According to Boswell, Eliock had studied in the Saxon city of Halle.1
Alexander Carlyle wrote in his autobiography that:
"Elliock was an excellent scholar, and a man of agreeable conversation, having many curious anecdotes in his store; and to his other fund, had the good fortune to be well acquainted with Frederick the Great of Prussia, when he retired into Holland from his father's tyranny, and visited him at least once by invitation, after he came to the throne."2