Brown's mother Joyce was a conductor, composer, and concert pianist, while his father Bud was an Ohio Congressman and chairman of the board of the Brown Publishing Company, the family-owned newspaper business started by his grandfather, Congressman Clarence J. Brown. He graduated from St. Albans School in Washington, D.C., and earned a scholarship to Northwestern University, where he became a member of the Sigma Chi Fraternity. He was inspired to become an actor by a neighbor who showed him Shakespeare's works.
Brown has been married to Jeanne Johnson since 1993; they have two children.
Brown is known for voicing Mr. Krabs in SpongeBob Squarepants, playing Byron Hadley in The Shawshank Redemption, Drill Sargent Zim in Starship Troopers, Lex Luthor in the DC Animated Universe, and Captain Black in Jackie Chan Adventures. He also voiced the Dark Dragon in American Dragon: Jake Long alongside other Avatar voice actors including Mae Whitman, Dante Basco, Lauren Tom, and Keone Young. He is also the voice of Destro in the animated series G.I. Joe: Renegades, Mr. Freeze in The Batman, Rhino in The Spectacular Spider Man, Savage Oppress in Star Wars: The Clone Wars, Odin in The Avengers: Earth's Mightiest Heroes, and the Thunder God Rayden in Mortal Kombat: Defenders Of The Realm. He also voices Silas in Transformers Prime.
In live action films, he has played a variety of villains, the most notable of these being The Kurgan, the immortal foe of Connor Macleod in the first Highlander film. He also played Meacham in the sci-fi action film Cowboys and Aliens.