Born in Ballencrieff, East Lothian, Murray travelled to North America and took part in the French and Indian War.

After the conflict, his administration of the Province of Quebec was noted for its successes, being marked by positive relationships with French Canadians, who were reassured of the traditional rights and customs.

[3] Educated in Haddington, East Lothian and Selkirk, Scottish Borders, he began his military career in 1736 in the Scots Brigade of the Dutch States Army.

In 1740 he served as a second lieutenant in John Wynyard's Regiment of Marines under his brother Patrick Murray, 5th Lord Elibank in the Battle of Cartagena de Indias.

Murray believed Wolfe's plan to land the army at Anse au Foulon was foolish and absurd, and succeeded "only by Providence".

As a result, the French managed to lay siege to Quebec but this had to be abandoned due to a lack of supplies and the arrival of a British relief fleet.

Murray's successful part in the British advance on Montreal in which he pacified many of the French Canadians, showed his true worth as a military commander and a negotiator.

On 5 September 1760, Murray signed a Treaty of Peace and Friendship with the Huron Nation, then residing at Lorette, near Quebec City.

During the American War of Independence, he defended Fort St. Philip, at Port Mahon, against a Franco-Spanish siege for seven months (1781–82), until forced to surrender.