There are 3 US Post Offices in Union County serving a total of 15,600 residents equating to 5,200 residents per post office. It's estimated that approximately 24,899 packages are handled across the 3 county post offices annually. Union County is a county located in the U.S. state of Tennessee. As of the 2010 census, the population was 19,109. Its county seat is Maynardville. Union County is included in the Knoxville, TN Metropolitan Statistical Area.