Cleburne is a city in Johnson County, Texas, United States. The population was 26,005 as of the 2000 census. It is the county seat of Johnson County. Cleburne is named for a Confederate General, Patrick Cleburne, who never lived in the area. Lake Pat Cleburne, the reservoir that provides water to the city and surrounding area, is also named for him. Cleburne apartments for rent comparison page shows most up to date rent information on Cleburne apartments and houses. Rent information is obtained from multiple rental sources but we cannot guarantee their accuracy.