Located in the eastern part of the county, it borders the following townships: Parts of the city of Logan, the county seat of Hocking County, are located in western Green Township.

Southeast of Logan lies the unincorporated community of Haydenville.

[4] It is one of sixteen Green Townships statewide.

[5] 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.

There is also an elected township fiscal officer,[6] who serves a four-year term beginning on April 1 of the year after the election, which is held in November of the year before the presidential election.