Wilson is a native of Atlanta, Georgia. He hitchhiked from Atlanta to Los Angeles with a friend in 1961 when he was nineteen years old. His friend eventually returned to Georgia, while Wilson enrolled in an acting class and pursued the craft as his profession.
Wilson made his screen debut portraying characters suspected of murder in his first two films. In his debut film, Wilson played a murder suspect in 1967's In the Heat of the Night, which starred Sidney Poitier, Rod Steiger and Warren Oates. His follow-up role, in the same year, was In Cold Blood, based on the book of the same name by Truman Capote. Wilson portrays real-life murderer Richard Hickock, while Robert Blake played his partner, Perry Smith. Director Richard Brooks cast Wilson and Blake in the starring roles specifically because they were unknown at the time. The director passed over better-known actors, including Steve McQueen and Paul Newman, for the parts. Wilson later explained Brooks' casting motivations: "Brooks hired two 'unknowns' and he wanted to keep it that way. We were treated like two killers he had somehow run across."
The film earned Wilson an appearance on the cover of Life Magazine, published on May 12, 1967. Wilson was just 24 years old at the time. The cover features Truman Capote standing between Wilson and Blake on an empty highway in Kansas. The caption, Nightmare Revisited, appears with them on the cover. Wilson appeared in The Great Gatsby in 1974 opposite Robert Redford. He received a 1980 Golden Globe nomination for Best Supporting Actor for his performance in The Ninth Configuration by director and friend William Peter Blatty. He lost the Golden Globe to Timothy Hutton. In 1995 Wilson got attention for his role as a prison chaplain in Dead Man Walking, starring Susan Sarandon and Sean Penn, based on the book of the same name by Sister Helen Prejean.
Wilson's long filmography also includes The Gypsy Moths, The Right Stuff, A Year of the Quiet Sun, Malone, The Grass Harp, Junebug, The Host, Monster, Young Guns II, Pearl Harbor, Big Stan, Judge Dredd, the Shiloh film series and Behind the Mask: The Rise of Leslie Vernon. Wilson has filmed on location in South Korea, Japan and Spain. Wilson had a recurring role in several episodes of CSI: Crime Scene Investigation as Sam Braun, father of crime-scene investigator Catherine Willows (portrayed by Marg Helgenberger). Braun was killed off in the episode "Built to Kill, Part 2". In the fall of 2011 he also made an appearance opposite Laura Dern in the HBO series, Enlightened.
Wilson was cast as Dr. Hershel Greene in the second season of The Walking Dead in June 2011. The role has earned him positive reviews, including a "cheer" from TV Guide, which wrote that he had contributed "subtle shades of humanity to the character of Hershel Greene." Wilson was offered the opportunity to join the show while visiting his 97-year-old mother in Georgia. He has described his mother as "a fan of the show."
Wilson reflected on his career in a 2011 interview with Access Atlanta's Rodney Ho: "It's been up and down. It's always been. You have dry spells. At different times, you are starting over. If you love it, you stay with it. That's what I'm doing. I've accomplished more than I would have hoped to have accomplished. I don't want to be a big movie star. I can be someone who walks the streets and not get mobbed. I want to be as fine an actor as I can be. I am still striving to be as good as I can be." Wilson was filming scenes for The Walking Dead in Senoia, Georgia, at the time the interview took place.