Born in Memphis, Tennessee, Browder grew up in Charlotte, North Carolina. His parents were race car owners and operators. He attended Furman University in Greenville, South Carolina and graduated with a degree in psychology. He was a star player on the Furman football team. Browder met his wife, actress Francesca Buller, while studying at the Central School of Speech and Drama in London. He and Francesca have a son and a daughter.

Browder appeared as a recurring guest on the U.S. television show, Party of Five as Sam Brody in its 3rd season in 1997. Browder and Buller moved with their two children to Australia during the production of Farscape (1999–2002), on which Browder starred as American astronaut John Crichton. Buller played several guest roles on the show. The two returned to the United States in 2003 following the cancellation of Farscape. He has received two Saturn Awards for Best Actor In A Television Role for his acting in Farscape. He appeared in the 2004 movie, A Killer Within, co-starring C. Thomas Howell and Sean Young. Also in 2004, he portrayed fellow actor Lee Majors in the made-for-TV film Behind the Camera: The Unauthorised Story of Charlie's Angels.

He returned to play John Crichton in the 2004 SciFi Channel mini-series, Farscape: The Peacekeeper Wars. The mini-series wrapped up the remaining plotlines of Farscape, while leaving open the possibility of future adventures. November 2004 marked the audiobook release of Interlopers, a novel written by Alan Dean Foster and narrated by Browder. In January 2005, Browder voiced the character Bartholomew Aloysius "Bat" Lash in an episode of the animated series Justice League Unlimited entitled "The Once and Future Thing, Part 1: Weird Western Tales".

Browder returned to the SciFi Channel as he joined the cast of Stargate SG-1 for its 9th season in 2005. He played the character of Lieutenant Colonel Cameron Mitchell, the team's new commanding officer. Browder's former Farscape co-star Claudia Black appeared on SG-1 as well in the 8th season episode entitled "Prometheus Unbound" and again during the first episodes of the 9th season, and then became a regular cast member on the series in its 10th season. Some episodes of Stargate SG-1 comically alluded to Farscape on several occasions during Browder and Black's time on the series.