Tesh has been married to actress Connie Sellecca since 1992. They have one daughter together named Prima. His wife also has a son named Gib, with actor Gil Gerard. Tesh resides in Los Angeles.
Tesh is a Christian. He was raised a Baptist and was involved in the church during his youth. He played organ, sang in the choir, and went to church camp. He became inactive in the church during his adult life, but became involved again after his future wife introduced him to pastor Louis Lapides. Since then, he has written and performed Christian music.