He sat as Member of Parliament for Edinburghshire from 1790 to 1801, and was Chief Baron of the Exchequer in Scotland from 1801 until his death in 1819.

He was the eldest son of Robert Dundas of Arniston, the younger and his second wife, Jean, daughter of William Grant, Lord Prestongrange.

(Hamilton 1888, p. 195)[1] With the help of his uncle Henry Dundas, 1st Viscount Melville he succeeded Alexander Wight as Solicitor General for Scotland in 1784 and became lord advocate in 1789.

In June 1792 he was the cause and focus of the Dundas Riots, starting at his home in George Square.

[3] Following the riots he made it a personal aim to prosecute and effectively destroy the Edinburgh lawyer, Thomas Muir of Huntershill, who he saw as responsible for most of the seditious mischief.