Located in the south central part of the county, it borders the following townships: No municipalities are located in Gasper Township.

[4] It was named after John Gasper Potterf (or Batdorf) (1758-1836),[5] A Pennsylvanian of German descent who became an early and wealthy settler of Preble County.

Gasper Township was originally part of Washington Township until Potterf convinced the Board of Commissioners to dissever the twenty-four sections of the southern part of Washington Township.

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,[6] 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.