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.
Biggs's other TV roles include the soap operas Ryan's Hope as Fenno Moore from 1988–1989, and General Hospital as Chad Wainwright in 1990. Another television role was on the 1990s TV series Stat.
Biggs appeared in the HBO docudrama Too Big To Fail on the 2008 financial crisis as Wells Fargo chairman Richard Kovacevich.
