[3] Located in the northern extension of the county, it borders the following townships: Part of the village of Mount Orab is located in southwestern Green Township.

It is named from a thicket of green bushes near the home of a pioneer settler.

[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.