Originally a native of Scotland, Edmiston came to Canada to settle in Clover Bar, Northwest Territories in the early 1880s. After living there for about ten years, he relocated to nearby Edmonton where he would employ himself as an architect, the first ever in the town. Engaging in a partnership with another fellow architect, his firm would design some of the first buildings in the newly developing town. He would also involve himself with the town's politics, sitting on the Edmonton Town Council, and later serving out two terms as Mayor of Edmonton, from 1897 to 1899. During his time as mayor, he involved himself in local affairs as well as run his architectural business. He would also lobby for a new bridge to be built over the North Saskatchewan River, connecting Edmonton with the town of Strathcona. He would voluntarily relinquish his position as mayor and not run in the 1899 election, opting to retire.