He was the second son of Lady Amelia Anne Sophia Stanley and John Murray, 1st Marquess of Atholl, a leading Scottish royalist and defender of the Stuarts during the English Civil War of the 1640s, until after the rise to power of William and Mary.

[1] His elder brother John Murray, who inherited their father's marquessate in May 1703, was created 1st Duke of Atholl in June 1703.

[2] By 1685, he was a Colonel in the Scots Greys before rising to become a general in the British Army.

[3] He was created Earl of Dunmore and Lord Murray of Blair, Moulin and Tillimet, and Viscount of Fincastle,[4] all on 16 August 1686 in the Peerage of Scotland.

[3] Through his daughter Lady Anne, he was a grandfather of William Cochrane, 5th Earl of Dundonald, Lady Anne Cochrane (who married James Hamilton, 5th Duke of Hamilton), Lady Susan Cochrane (wife of Charles Lyon, 6th Earl of Strathmore and Kinghorne, and, after his death, George Forbes, Master of the Horse, to Prince Charles Edward Stuart),[8] and Lady Catherine Cochrane (wife of Alexander Stewart, 6th Earl of Galloway).