Norris was born in South Bend, Indiana, to Jack, a furniture store owner, and Rosie Norris. He has four sisters. Norris graduated from Clay High School and in 1985 from Harvard College, where he majored in social studies.

He also attended the Royal Academy of Dramatic Art.

Norris's limp is a result of an accident in his early childhood when he was severely injured while playing soccer with his sisters.

When the ball rolled into the street, Norris's leg was crushed by an oncoming police car, who was unable to see the young Norris running into the street. This limp is portrayed in his role in The Firm, as well as in Breaking Bad.

Prior to Breaking Bad, Norris starred in Tremors: The Series as W.D. Twitchell, and in the movie "Without Limits". He has also had guest spots on shows such as NYPD Blue, The X-Files, CSI: Crime Scene Investigation, The West Wing, Nip/Tuck, Married With Children, Las Vegas, Castle, 24, Terminator: The Sarah Connor Chronicles, Eagleheart, True Blood, Bones, Grey's Anatomy, Lost, Nash Bridges, NCIS, Six Feet Under, Medium and Charmed and appeared in movies such as Gattaca, The Negotiator, The Lawnmower Man, Little Miss Sunshine (along with Bryan Cranston), Evan Almighty, Terminator 2: Judgment Day, Lethal Weapon 2, Total Recall (as the mutant Tony), Lakota Woman: Siege at Wounded Knee, Liars' Dice, The Cell, Hard to Kill, Playmaker, 3 Strikes, American Gun, and Barbarians at the Gate: The Fall of RJR Nabisco.

He also played the commanding officer at the military training camp in the film Starship Troopers. He is currently in his fifth and final season as Hank Schrader on Breaking Bad as well as starring in the CBS series Under the Dome based on the Stephen King novel.