However, on 7 February 1764, the House of Lords deemed Murray the rightful heir to his uncle's title (notwithstanding the attainder of his father) and he succeeded him as 3rd Duke of Atholl.
His wife, on the death of her father, the second duke, succeeded to the suzerainty of the Isle of Man, and to the ancient English barony of Strange, of Knockyn, Wotton, Mohun, Burnel, Basset, and Lacy.
For some time negotiations had been in progress with the British government for the revestment of the suzerainty back to the British crown; and in an act of parliament, the Isle of Man Purchase Act 1765, was passed to give effect to a contract between the lords of the Treasury and the Duke and Duchess of Atholl for the purchase of the sovereignty of Mann and its dependencies for £70,000, the duke and duchess retaining their manorial rights, the patronage of the bishopric and other ecclesiastical benefices, the fisheries, minerals, etc.
The arrangement rendered them very unpopular in Mann, and the 42nd Regiment of Foot, or Black Watch, under Lord John Murray, had to be stationed in the island to maintain order.
The money received by the duke and duchess was directed to be laid out and invested in the purchase of lands of inheritance in Scotland, to be inalienably entailed on a certain series of heirs.