Located in the northeastern corner of the county, it borders the following townships: West Virginia lies across the Ohio River to the east: Wood County to the northeast, and Jackson County to the southeast.

It is the farthest upstream of Meigs County's Ohio River townships.

No municipalities are located in Olive Township, but three unincorporated communities lie there: Statewide, the only other Olive Township is located in Noble County.

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,[4] 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.