Russell was born at Woburn Abbey, Bedfordshire, the seventh son of John Russell, 6th Duke of Bedford and his second wife, Lady Georgina (or Georgiana) Gordon, daughter of Alexander Gordon, 4th Duke of Gordon, although it has been claimed that Russell's father was actually the Victorian painter Sir Edwin Landseer, who conducted a lengthy affair with the Duchess of Bedford.

[2] Russell joined the Army on 11 July 1839 when he purchased a commission as a Second Lieutenant in the Rifle Brigade.

Russell was a Colonel in the Rifle Brigade and served during the Siege of Sevastapol in the Crimean War.

He became General Officer Commanding South-Eastern District in April 1877[3] and Commander of the British Troops in Canada in May 1883[4] and was advanced to Knight Grand Cross of the Order of the Bath (GCB), having previously been a Companion of the Order of the Bath (CB).

He was not however styled Sir Alexander Russell since he already held the higher title of Lord due to his father being first a Marquess and later a Duke.