He was the second but only surviving son of William Cochrane of Kilmaronock, MP for Wigtown Burghs, and the former Lady Grizel Graham.
[1] His paternal grandparents were William Cochrane, Lord Cochrane and his wife Lady Katherine Kennedy (a daughter of John Kennedy, 6th Earl of Cassilis).
His maternal grandparents were James Graham, 2nd Marquess of Montrose and the former Lady Isabel Ker (widow of Robert Ker, 1st Earl of Roxburghe, and fifth daughter of William Douglas, 7th Earl of Morton).
[1] Together, they were the parents of: Lord Dundonald died at Paisley Abbey on 28 May 1737,[1] and was succeeded in his titles by his eldest son, William.
On the death of his unmarried heir in 1758, his line died out and the title was inherited by his son's second cousin, Thomas Cochrane.