There are 7 US Post Offices in Obion County serving a total of 26,221 residents equating to 3,746 residents per post office. It's estimated that approximately 41,852 packages are handled across the 7 county post offices annually. Obion County is a county located in the U.S. state of Tennessee. As of the 2010 census, the population was 31,807. The county seat is Union City. The county was formed in 1823 and organized in 1824. It was named after the Obion River. Obion County is part of the Union City, TN\u2013KY Micropolitan Statistical Area, which is also included in the Martin-Union City, TN-KY Combined Statistical Area."