He was born in Liverpool on 14 March 1836. He was educated at the Liverpool Collegiate School and Cheltenham College. He attended the Royal Military Academy, Woolwich and was commissioned as an officer in the Royal Engineers in 1855.
His first appointment was as secretary to the British Boundary Commission in 1858, whose duty it was to map the 49th parallel between the Rocky Mountains and the Pacific Ocean. He spent four years in North America, during which time he documented his travels in a diary, the transcription of which can be found in "Mapping the Frontier" edited by George F. G. Stanley.
In 1864 he started working on the Ordnance Survey of Jerusalem funded by the wealthy Angela Burdett-Coutts, 1st Baroness Burdett-Coutts whose primary motivation was to find better drinking water for those living in the city. During the resulting search, he produced the most accurate map of Jerusalem and identified the eponymous Wilson's Arch but was unable to find a new source of water. According to a book published in 2013, "Wilson was the first to pay proper scholarly attention to the stonework of the Haram el-Sharif (Temple Mount) walls when [conducting] the first comprehensive mapping of the Old City (the Ordnance Survey of Jerusalem)". Over a century after Wilson's work, The Jerusalem Post commented that his efforts "on the Jerusalem Ordnance Survey served as the basis for all future Jerusalem research".
Also in 1867, with the Palestine Exploration Fund, Wilson had a leading role in the PEF Survey of Palestine and conducted one of the first major Excavations at the Temple Mount in Jerusalem. In 1868 he joined the Ordnance Survey of Sinai. In 1872 he was elected to the Society of British Archaeology.
He served director of the Palestine Pilgrims' Text Society, an organization that publishing texts and translations related to pilgrimages to the Holy Land. He was chairman of the Palestine Exploration Fund from 1901 until his death in 1905.
After returning home, Wilson was appointed to the Ordnance Survey of Scotland in 1867 and also acted as Assistant Commissioner on the Borough Boundary Commission. In 1874 he became a Fellow of the Royal Society. He became director of the topographical department at the British War Office and assistant quartermaster-general in the British Intelligence Department. In 1876 he received an Order of the Bath. He then headed the Ordnance Survey of Ireland.
From 1879 to 1882, he was consul-general in Anatolia and traveled extensively in Turkey. In the summer of 1882, he took part in Garnet Wolseley's expedition to put down the rebellion of Colonel 'Urabi.
From 1884 to 1885, Wilson took part in the Khartoum Relief Expedition, commanded by Garnet Wolseley. He was part of the advance rescue force led by Sir Herbert Stewart. After Stewart was mortally wounded Brigadier-General Wilson took command of this group of about 1,400 men. On two Nile steamers Wilson's Desert Column reached Khartoum in the afternoon of 28 January 1885. It came two days too late: Khartoum had been seized by the Mahdists in the early hours of 26 January. Between 5,000 and 10,000 inhabitants were slaughtered, among them Major-General Charles George Gordon. Wilson received criticism afterwards for his delay in sailing to Khartoum, with one author stating that he had "lost any nerve he had ever possessed". Other sources however, spread the blame, particularly on the commander, Garnet Wolseley, 1st Viscount Wolseley who had already accused Wilson. The public in England also blamed Prime Minister William Gladstone for not having taken steps to relieve the siege of Khartoum and some historians have held Major-General Gordon responsible, because he had refused the order to evacuate while that was still possible.
He died on 25 October 1905 at Tunbridge Wells. A subsequent biography on Wilson, by Sir Charles Moore Watson, said that he "probably did more than any other man to increase the knowledge of the geography and archeology of Asia Minor, Palestine and the adjacent countries".