Greene County is a county in the U.S. state of Alabama. As of the 2010 census, the population was 9,045. making it the least populous county in Alabama. Its county seat is Eutaw. Its name is in honor of Revolutionary War General Nathanael Greene of Rhode Island.HistoryGreene County was established on December 13, 1819. It is the least populated county in Alabama.GeographyAccording to the U.S. Census Bureau, the county has a total area of, of which is land and (1.9%) is water.Major highways20px20px Interstate 20/Interstate 5920px U.S. Route 1120px U.S. Route 4320px State Route 1420px State Route 39