Burke was born in New Orleans, the son of Santa Maria (Palermo) and Martin Joseph “Marty” Burke, a boxer who fought Gene Tunney and later owned a restaurant and a nightclub known as “Marty Burke’s” in the New Orleans French Quarter. He was of Irish and Italian descent. After training at the Pasadena Playhouse, Burke’s film career began with a small role in the movie Golden Girl. Early in his career, Burke guest starred in the syndicated series, Highway Patrol and Men of Annapolis. In 1956–1957, Burke was cast as Dr. Noah McCann in Noah’s Ark, a Jack Webb-produced weekly program which aired on NBC, the story of a pair of dedicated veterinarians. Victor Rodman played the older colleague, Dr. Sam Rinehart. In the 1957–1958 season, Burke appeared as Jeff Kittridge in five episodes of Barry Sullivan’s adventure/drama series, Harbormaster. Burke also guest starred on episodes of Tightrope, Dragnet, Adventures of Superman, The Man and the Challenge, and M Squad. In the 1959–1960 season, he appeared as Robertson in the NBC espionage series Five Fingers, starring with David Hedison. After Five Fingers, Burke was cast in the lead role of the police show Naked City, in which he appeared as Adam Flint from 1960 to 1963. Burke then appeared in the starring role of Captain (later Major, then Colonel) Joe Gallagher on 12 O’Clock High between 1964 and 1967, during which time he met his wife, Lyn. The 12 O’Clock High role was Burke’s last lead television role. In 1967, Burke starred in the film Valley of the Dolls as Lyon Burke, the young lawyer who befriended all three female stars and had a tempestuous relationship with Anne Welles. He also played a police officer who pursued an art thief played by Steve McQueen in The Thomas Crown Affair. During the 1970s, he appeared in three episodes each of ABC’s The Love Boat and CBS’s Medical Center. In 1984, he appeared as C.C. Capwell in twenty-one episodes of the NBC soap opera Santa Barbara. He appeared in supporting roles in a number of television series, including recurring roles in Dynasty from 1982–1988 and in Tom Selleck’s Magnum, P.I. from 1981–1985 as Rear Admiral Hawkes. Burke also served as a television commercial spokesman for the Radio Shack electronics retailer. Burke retired from acting in the early 1990s. He was the grandfather of actress Alia Shawkat. Suffering from leukemia and non-Hodgkins lymphoma, he died at his home in Palm Springs, California. His second wife, known professionally as Lyn Peters, died in Palm Springs on September 10, 2013, at the age of seventy-two.