Palouse is a city in Whitman County, Washington, United States. The population was 1,015 at the 2020 census. Palouse was first settled i…Palouse is a city in Whitman County, Washington, United States. The population was 1,015 at the 2020 census. Palouse was first settled in 1869 by William Ewing. The townsite was founded in 1875 by W.P. Breeding.