Burleson is a city in Johnson and Tarrant counties in the U.S. state of Texas. It is a suburb of Fort Worth. At the 2010 census it had a popul…Burleson is a city in Johnson and Tarrant counties in the U.S. state of Texas. It is a suburb of Fort Worth. At the 2010 census it had a population of 36,690, and in 2019 it had an estimated population of 48,225. By the 2020 census, its population grew to 47,641 with a 2021 census-estimated population of 51,618.