Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Green Township is one of the ten townships of Fayette County, Ohio, United States. The 2000 census found 499 people in the township. It is one of sixteen Green Townships statewide. 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.