Woudenberg was born on February 15, 1945 in the German village of Elspe. He was the grandson of NSB leader Hendrik Jan Woudenberg and the son of Jan Woudenberg, who served in a Dutch unit of the Waffen-SS and was killed in Poland shortly before his birth. In 2004, he played a performance about this background by his childhood friend Ischa Meijer, who survived the Bergen-Belsen camp as a child.
Woudenberg was one of the founders of Het Werkteater, an innovative theater collective. He became known for his role in Blue Movie (1971), but has appeared in many theater performances, TV series and films.