[3] Located in the southeastern corner of the county along the Ohio River, it borders the following townships: Lewis County, Kentucky lies across the Ohio River to the southwest.

The village of Rome is located in central Green Township along the Ohio River.

[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.