Robert Dundas was born on 30 July 1761, the eldest son of the Rev. Robert Dundas and his wife Elizabeth, daughter of the Rev. Thomas Turnbull. On 20 July 1798 he married Matilda, daughter of the Hon. Archibald Cockburn, a Baron of the Court of the Exchequer in Scotland; they had one son and six daughters. Robert Dundas was one of the Principal Clerks of the Court of Sessions in Scotland, and was created a baronet on 24 August 1821. He died on 28 December 1835, and was succeeded by his son David as 2nd baronet.