Green Township is one of the ten townships of Fayette County, Ohio, United States.

Located in the southwestern corner of the county, it borders the following townships: No municipalities are located in Green Township.

It is one of sixteen Green Townships statewide.

[4] 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,[5] 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.