Washington is a city in, and the county seat of, Washington County, Kansas, United States. As of the 2020 census, the population of the …Washington is a city in, and the county seat of, Washington County, Kansas, United States. As of the 2020 census, the population of the city was 1,071. Washington was established in spring 1860, and in the same year was named the county seat. Until the end of the Civil War, it was protected by two stockaded buildings, the Washington Company House and Woolbert's Stockade Hotel.