Located in the far south of the county along the Ohio River, it borders the following townships: Greenup County, Kentucky lies across the Ohio River to the west.

No municipalities are located in Green Township, although the census-designated place of Franklin Furnace lies in the northeastern part of the township, and the unincorporated community of Haverhill lies in the south of the township.

[6] Green Township comprises most of the land that was the French Grant that was paid out by Congress in 1785 to French colonists were defrauded by the Scioto Company.

[7][8] 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,[9] 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.