Born Roy Barnes Jones in Dade City in Pasco County, near Tampa, Florida, he began his acting career on the stage, first appearing on Broadway in May 1931 before making his motion picture debut in Gold Bricks, a 1936 two-reel comedy short released by 20th Century-Fox. He appeared in numerous films in secondary parts and returned to perform on Broadway in such productions as Twentieth Century, My Sister Eileen, and Carnival in Flanders until he began making guest appearances on television series. After appearing on Gale Storm's My Little Margie in 1956, he became part of several television series for which he is best remembered. In a show that was the precursor to The Love Boat, Roberts played the ship's captain for four years in Storm's next hit, Oh! Susanna, which aired on CBS and ABC from 1956 to 1960. He guest-starred in scores of series, including the western-themed crime drama, Sheriff of Cochise, the western series, My Friend Flicka, The Life and Legend of Wyatt Earp (as Texas cattle baron Shanghai Pierce), and The Travels of Jaimie McPheeters, and Brian Keith's Cold War drama, Crusader. Roberts appeared on four episodes of the CBS legal drama, Perry Mason, including the role of murderer Arthur Janeel in the 1961 episode, "The Case of the Malicious Mariner."

In the 1940s and 1950s, Roberts was a regular in many films noir, including Force of Evil (1948), He Walked by Night (1948), Nightmare Alley (1947), The Brasher Doubloon (1947), Borderline (1950) and The Enforcer (1951). In 1953 he appeared as Vincent Price's crooked Business partner (and first victim) in House of Wax. In 1956 he was Colonel Sam Sherman in The First Texan. He also appeared in the neo-noirs The Outfit (1973) and Chinatown (1974). He also had a small role in the hit 1963 Stanley Kramer comedy, It's a Mad, Mad, Mad, Mad World as a police officer. Unfortunately, his role was cut from later television and movie versions to reduce running time. However, because of an interest in restoring IAMMMMW to its original length, Roberts' brief role has seen life again in versions made for laserdisc and extended-length DVDs.

During the middle 1960s, Roberts was one of the most recognizable faces on television, and had recurring roles concurrently on a number of popular programs, including:

Roberts appeared in an episode of the situation comedy A Touch of Grace in 1973. His last television appearance was on the 21 January 1974 CBS broadcast of Here's Lucy. In that installment, "Lucy Is N.G. As An R.N.", Roberts played a Veterinarian.

Roberts died in Los Angeles, California, of a heart attack on 28 May 1975 and was interred at Greenwood Memorial Park in Fort Worth, Texas.