Rogersville is a city in Greene and Webster counties in the U.S. state of Missouri. As of the 2020 census, its population was 3,897. Rogersvill…Rogersville is a city in Greene and Webster counties in the U.S. state of Missouri. As of the 2020 census, its population was 3,897. Rogersville was named after Doctor Rogers, a pioneer settler. A post office called Rogersville has been in operation since 1882. The Citizens Bank of Rogersville was formed as a corporation on December 15, 1908, with $10,000 in capital stock.