Born in Cape Town, Wenning was educated at Texas Christian University (Master of Divinity) in Fort Worth, Texas and New York University (master's in both psychology and counseling). From 1969 to 1977, he was pastor of a Presbyterian church in Durban, South Africa. In 1977 he returned to the United States where he worked for the next three decades as a pastor in various Presbyterian Church (U.S.A.) congregations, including one in Pittsburgh, Pennsylvania.
He was notably the senior pastor at Bel Air Presbyterian Church from 1995 to 2001. There he developed a close relationship with church members Ronald and Nancy Reagan. He notably conducted President Reagan's interment service on June 7, 2004 following the latter's death and state funeral.