There are 5 US Post Offices in Greene County serving a total of 45,955 residents equating to 9,191 residents per post office. It's estimated that approximately 73,349 packages are handled across the 5 county post offices annually. Greene County is a county located on the eastern border of the U.S. state of Tennessee. As of the 2010 census, the population was 68,831. Its county seat is Greeneville, and the current county mayor is David Loy Crum (R). Greene County comprises the Greeneville, TN Micropolitan Statistical Area."