Located in the western part of the county, it is composed of several small "islands", separated due to municipal annexations.

These islands border the following townships and cities: Most of Norwich Township has been annexed by the cities of Columbus (the county seat of Franklin County), in the south, and Hilliard, in the north.

Statewide, the only other Norwich Township is located in Huron County.

It was named by Thomas Backus, a prominent early resident and native of Norwich, Connecticut.

[5] 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.