Wheeler was born at Farmers Creek in Lapeer County, Michigan and attended the common schools.

He enlisted in the Union Army, November 1, 1861, as a private in Company C, Tenth Regiment, Michigan Volunteer Infantry.

In 1890, was elected as a Democrat from Michigan's 9th congressional district to the 52nd United States Congress, defeating incumbent Republican Byron M. Cutcheon.

Harrison H. Wheeler was appointed United States pension agent at Detroit on February 8, 1894, and served until his death.

He died at Farmers Creek, near Lapeer and is interred in Lakeview Cemetery of Ludington.