Born in Portsmouth, Ohio, he graduated from Portsmouth High School in 1939. He received his B.A. from Kenyon College in Gambier, Ohio in 1943, where he was initiated into Sigma Pi Fraternity, and his LL.B. from Western Reserve University in Cleveland, Ohio in 1947. From 1942 to 1944, he was in the United States Marine Corps. After his admission to the bar on March 6, 1947, he was the city of Portsmouth's assistant solicitor until 1951, when he was elected Scioto County Prosecuting Attorney. He served one four year term. In 1961, he was elected to Congress and served twenty years there. He was succeeded by Bob McEwen, who had managed two of his re-election campaigns.
After his retirement from Congress, he was a consultant in Washington, D.C. from 1981 to 1986, when he returned to Portsmouth and resumed his law practice.
An artificial lake on the East Fork of the Little Miami River in Clermont County near Batavia is named for him (see East Fork State Park), as is the William H. Harsha Bridge, which spans the Ohio River between Ohio and Kentucky.
Harsha's son, William H. Harsha III, is a judge of the Ohio Court of Appeals for the Fourth Appellate District.