Located in the south central part of the county, it borders the following townships: Most of the village of Caldwell, the county seat and by far the biggest village of Noble County, is in northern Olive Township.

A small corner of the village of Dexter City is also in the township's far southeast.

Statewide, the only other Olive Township is in Meigs 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.