Biggs was born on April 4, 1955 in Toledo, Ohio. When he was very young, he was a foster child. He decided to pursue acting when he was a student at Central Catholic High School (Toledo, Ohio). He received a BFA from Juilliard in 1977 and first did some guest roles in television shows. In 1995 he was nominated for the role of Damar in the science fiction show Star Trek: Deep Space Nine. First intended as a minor character, Damar later became one of the major figures in the show, leading the entire Cardassian Union and having a major influence on the show's events.