There are 2 US Post Offices in Johnson County serving a total of 9,201 residents equating to 4,601 residents per post office. It's estimated that approximately 14,686 packages are handled across the 2 county post offices annually. Johnson County is a county located in the U.S. state of Georgia. As of the 2010 census, the population was 9,980. The county seat is Wrightsville. Johnson County is part of the Dublin, GA Micropolitan Statistical Area."