Located in the southeastern part of the county, it borders the following townships: •
Richland Township - north corner •
Wayne Township - northeast •
Fairfield Township, Highland County - southeast, north of Penn Township •
Penn Township, Highland County - southeast, south of Fairfield Township •
Union Township, Highland County - south •
Clark Township - southwest •
Washington Township - west •
Union Township - northwest The entire township lies in the
Virginia Military District. The village of
New Vienna is located in the southeastern part of Green Township, along the Highland County line. Green Township contains the unincorporated community of
New Antioch. ==Name and history==