William Armstrong was born in Dublin, Ireland. He studied art in Ireland, then completed an apprenticeship in England with the Midland Railway to become a railway engineer. He emigrated to Canada in 1851, settling in Toronto and began work with the railway. He found a market for his artwork with the illustrated news who covered the events in the colonies. His watercolours of local events and scenes were reproduced as monochrome wood engravings so they could be included in these weekly periodicals.
Armstrong marketed his skill as a draftsman as an asset to those who were interested in expanding Canada westward. Beginning in 1859, Armstrong made a number of trips west accompanying various survey expeditions. His drawings were used to report the activities of the expeditions as well as the terrain and human activity observed.
He won numerous prizes as an artist at provincial exhibitions, and his work was displayed at the Exposition Universelle in Paris in 1855, and at the Dublin International Exhibition, 1865. He exhibited with the Ontario Society of Artists and was a member of the Royal Canadian Academy of Arts until 1887, when he resigned.
A number of his watercolour landscapes of the Great Lakes may be found in collections such as the Art Gallery of Ontario, the National Gallery of Canada, and the Thunder Bay Historical Museum. He painted the watercolour The Arrival of the Prince of Wales at Toronto which hangs in the National Gallery of Canada in Ottawa, Ontario. Armstrong depicted grim working conditions inside Victorian Toronto’s industrial plants in his pastel drawing Toronto Rolling Mills, which forms part of the Toronto Public Library’s J. Ross Robertson Collection. His watercolour painting, Thunder Cape, Lake Superior, hangs in the National Archives of Canada.
In 1864 Armstrong began to teach drawing at the Toronto Normal School. He taught at the University of Toronto from 1872 to 1877. He retired in 1897 but continued teaching art from his home until his death. He died in Toronto on 9 June 1914.