Educated at Banff and Edinburgh, he emigrated to Van Diemen's Land (later Tasmania) in 1829, studied practical engineering and afterwards became a ship's officer.

He entered politics in October 1859 as member for Hobart in the legislative council, and in January 1863 joined the Whyte cabinet as minister without portfolio.

In 1868, at the time of the visit of the Duke of Edinburgh, Wilson was mayor of Hobart and on 4 August 1869 became premier and colonial secretary in a ministry which lasted until November 1872.

"[citation needed] In 1872, Wilson was elected president of the Tasmanian Legislative Council, and held this position until his death on 29 February 1880, on his "seventeenth" birthday aged 68.

Tasmania passed an intercolonial free trade act in 1870 during his premiership, but the question made no headway on the mainland.