Washington County is a county located in the U.S. state of Nebraska. As of the 2010 census, the population was 20,234. Its county seat is Blair.Washington County is included in the Omaha-Council Bluffs, NE-IA Metropolitan Statistical Area.In the Nebraska license plate system, Washington County is represented by the prefix 29 (it had the twenty-ninth largest number of vehicles registered in the county when the license plate system was established in 1922).