BRIAROAKS, TEXAS. Briaroaks is a residential community located on Interstate Highway 35W about fourteen miles south-southeast of Fort Worth and eleven miles northeast of Cleburne in northern Johnson County. The town began as a country subdivision in the late 1960s and early 1970s and incorporated in April 1971. In 1975 the population estimate was 390, and that number increased to 592 in 1980. In 2000 the population was 493. Briaroaks has a mayor-council form of government, and police and fire departments serve the primarily residential area.