Mesquite, TX. Mesquite is a city located within the Dallas/Ft.Worth area of Texas. As of the 2010 US Census, the population was 139,824. The city was founded May 22, 1873, by a Texas & Pacific Railway engineer who purchased land along the Texas & Pacific line outside of Dallas. The railroad, which ran from Dallas to Shreveport, began stopping at the newly-created town shortly thereafter, and the city began to grow around the railroad.