Born in Santa Barbara, California, Edwards has been cast in various movies and television shows, including Top Gun, ER and Northern Exposure. He reportedly earned $35,000,000 for three of his eight seasons on ER. He has been married to Jeanine Lobell since 1994, and they have four children.

Edwards was the youngest of five children and was encouraged by his parents to follow his interest in acting. He studied acting at University of Southern California but dropped out when parts were offered to him. His first starring role was in the comedy Revenge of the Nerds as Gilbert Lowell, though he had a tiny part in the 1982 film Fast Times at Ridgemont High, credited as "stoner Bud". It was his role as 'Goose' alongside Tom Cruise in the 1986 film Top Gun that brought his first widespread public acknowledgement and as a terminally ill patient in Hawks alongside with Timothy Dalton. However, his best known role to date is as Dr. Mark Greene on the long-running TV series ER. He once commented that it was challenging to play a character who was more intelligent than he himself was.