The shotgun - dubbed the "Holy Grail" - was made in April 1891 for John Adrian Louis Hope, 1st Marquess of Linlithgow and the seventh Earl of Hopetoun.
The three-barrelled ejector, 16-bore gun, with three triggers, was designed by renowned Edinburgh gun makers John Dickson & Son and is the only one of its kind.
Its origins were identified after the gun was taken to a valuing event at Hopetoun House, South Queensferry, and it has now been sold at Holt's auction in London, to a private collector, after fierce bidding from around the world.
Holt's founder, Nicholas Holt, said: "This is completely unique - the holy grail for any shotgun collector.
"The gun maker, which still exists in Edinburgh, looked back in their records and found this was the only single 16-bore, round action side by side by side ejector ever made. The mechanism was too complex to make more, but it still works fantastically well today and is capable of shooting three gamebirds with its three barrels."
Hope, a grand statue of whom stands in Melbourne, was educated at Eton and the Royal Military Academy at Sandhurst, but chose to pursue a life of leisure rather than a career in the army.
He became a Conservative Whip in the House of Lords in 1883, and served as Lord in Waiting. He was appointed Governor of Victoria in 1889, and due to his popularity with leading Australian politicians, he was made first Governor-General in July 1900.