Wepper married Angela von Morgen in 1979. His daughter, Sophie is also an actress, they appeared together in the crime series Mord in bester Gesellschaft between 2007 and 2017. Wepper made headlines in the yellow press when he left his wife Angela for the younger Susanne Kellermann (born 1974) in 2009. He has a daughter (born 2012) from the relationship with Kellermann, but later returned to his wife. Angela von Morgen died in January 2019, aged 76, following a cerebral haemorrhage. In 2020, Wepper married Susanne Kellermann.
