Tonasket is a city in Okanogan County, Washington, United States. The population was 1,103 at the 2020 census. Tonasket was officially inc…Tonasket is a city in Okanogan County, Washington, United States. The population was 1,103 at the 2020 census. Tonasket was officially incorporated on December 16, 1927. It is named after Chief Tonasket of the Okanogan people, a local leader from this area who assumed the status of grand chief of the American Okanogan after the drawing of the Canada–United States border by the Oregon Treaty of 1846, assuming a leadership role in Okanogan territory formerly held by Chief Nicola who lived north of the border.