The son of Thomas Douglas, 5th Earl of Selkirk and Joan Wedderburn-Colville, he was born in London. He was educated at Eton College and Christ Church, Oxford, graduating with First Class honours in Mathematics.
He was invested as a Fellow of the Royal Society in 1831.
He held the office of Lord-Lieutenant of the Stewartry of Kirkcudbright between 1844 and 1885.
He died at Saint Mary's Isle, Kirkcudbrightshire, in 1885, and the title of Earl of Selkirk devolved on the 12th Duke of Hamilton. The subsidiary title of Lord Daer and Shortcleuch became dormant.