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.

[4] Formerly part of Highland County, the land was transferred by the Ohio General Assembly so that Clinton County would have the constitutionally mandated 400 square miles (1,000 km2) of territory.

The township was created by the Clinton County Commissioners on August 21, 1813.

[citation needed] The township is governed by a three-member board of trustees, who are elected in November of odd-numbered years to a four-year term beginning on the following January 1.