Wogaman was born the second son of a Methodist minister in Toledo, Ohio, and lived in several Ohio communities as his father moved from parish to parish, until his father's respiratory condition forced the family's move to southern Arizona.
He was a professor of Bible and social ethics at University of the Pacific from 1961–66, where he had previously earned his B.A.
Outside of theological circles, Wogaman is perhaps best known as one of the religious leaders who counseled President Bill Clinton, who attended Foundry Church during his terms as U.S.
A United Methodist Minister (ordained in 1957), he was a delegate to that denomination's General Conference four times.
After retirement from Foundry Church in 2002, Wogaman served as Interim President of Iliff School of Theology, Denver, Colorado (2004–06) and as interim Senior Pastor of St. Luke United Methodist Church, Omaha, Nebraska (2008–09).