He was a younger son of Sir Robert Murray, Lord Provost of Edinburgh.
He was granted brevet rank as colonel on 1 June 1693 and made lieutenant-colonel of the Scots Foot Guards on 13 November 1695.
On 30 May 1697 Murray was appointed colonel of a Scots regiment in the Dutch States Army.
He served throughout the campaigns of the Duke of Marlborough, and at the time of his death was Governor of Tournai.
Robert Murray's only surviving son by his wife Marguerite Therese Booninck was Sir Joseph Murray, 3rd Baronet, also a soldier, who was created a Count of the Holy Roman Empire in 1761.