 Cochrane was the second son of Thomas Cochrane, 11th Earl of Dundonald, and Louisa Harriet, daughter of William Mackinnon, and the younger brother of Douglas Cochrane, 12th Earl of Dundonald.He was educated at Eton and Cheltenham College.Cochrane was an honorary lieutenant colonel of the 4th Battalion Argyll and Sutherland Highlanders, and served in the 93rd Highlanders and the Scots Guards.