He attended Oxford University and graduated from Temple University in Philadelphia, where he was a member of Sigma Pi fraternity, in 1943 with a bachelor's degree in education. While at Temple he did not participate in the university's theater program but spent his time working as a disc jockey for radio stations KYW, WFIL, and WIP.

His first screen role was a minor part in the film Winged Victory (1944). In 1947, he had a small but important role in the movie The Farmer's Daughter, the film that won Loretta Young her Best Actress Oscar. Andes, Lex Barker and James Arness played the title character's powerfully built and highly protective brothers.

On November 30, 1946, Andes married Jean A. Cotton, a nurse, in Upper Darby, Pennsylvania. The couple divorced in 1961.

In 1947, Andes received a Theater World Award for his debut performance in The Chocolate Soldier.

In 1952, he appeared as Marilyn Monroe's sweetheart and Barbara Stanwyck's brother in the cult film Clash by Night (directed by Fritz Lang and co-written by Clifford Odets). He co-starred with Angela Lansbury in the 1954 film noir A Life at Stake after appearing in 1952 with Robert Newton in Blackbeard the Pirate. In 1958, Andes starred as crusading former Louisiana State Police Superintendent Francis Grevemberg in the film Damn Citizen. His co-stars were Margaret Hayes as Dorothy Maguire Grevemberg and Gene Evans as police Major Al Arthur. In 1970, he appeared as Chief of Staff of the United States Army, General George C. Marshall, in the film Tora, Tora, Tora .

An episode of Playhouse 90 brought Andes to television on August 22, 1957. He played a Teacher in "Homeword Borne."

On television, from 1959 to 1960, Andes portrayed Frank Dawson in the syndicated police drama, This Man Dawson, the story of a former United States Marine Corps colonel who is hired to halt police corruption in a large, unnamed city. william Conrad did the series narration.

On Broadway, Andes was in Kiss Me, Kate and starred opposite Lucille Ball in the musical Wildcat in 1960, and later appeared on her 1960s sitcom, The Lucy Show. He later toured as Cervantes/Quixote in Man of La Mancha.

Later in 1963, Andes was cast as the lawyer-husband on the 1963 Desilu CBS sitcom, Glynis, starring Glynis Johns as his wife, a mystery Writer and amateur sleuth. The next year, he guest-starred in Mickey Rooney's short-lived Mickey sitcom on ABC.

Andes starred as the manager of a radio station in the serial Paradise Bay, which debuted September 27, 1965.

In his nearly five decades as an actor, Andes appeared in episodes of Cannon, Death Valley Days, Daniel Boone, I Spy, The Andy Griffith Show,The Rifleman, Perry Mason (in the episodes "The Case of the Skeleton's Closet" and "The Case of the Illicit Illusion"), The Outer Limits (in the episode "Expanding Human"), and Star Trek (in the episode "The Apple"). His work included voice acting in the animated Birdman and the Galaxy Trio (1967). Late in his career, he appeared in films such as ...And Justice for All and Tora! Tora! Tora! (about the Japanese attack on Pearl Harbor). He also appeared as Prime Minister Darius in the Buck Rogers in the 25th Century episode "Buck's Duel to the Death".

On November 11, 2005, Andes was found dead at the age of 85 at his home in Newhall, Santa Clarita, California. He had been suffering from bladder cancer and other ailments and committed suicide by asphyxiation, according to a report from the Los Angeles County Coroner's Office. His remains were donated to medical science.