Burton is a city in Washington County, Texas, United States. Prior to the 2010 census, Burton changed its status from a town to a city. The po…Burton is a city in Washington County, Texas, United States. Prior to the 2010 census, Burton changed its status from a town to a city. The population was 294 at the 2020 census. Burton was established in 1870 by John M. Burton; a native of Greensboro, Georgia. In June 1869, Burton sold land to trustees of the Houston and Texas Central Railroad and then sold to citizens. The arrival of the railroad after the Civil War benefited the community. The town received its first postmaster on September 23, 1870. By 1910, its population was 600. The community was incorporated on October 25, 1972.