The Irish-born star passed away on 12 December following a suspected heart attack in Thousand Oaks, California.
Davis began his career on stage in his native Ireland, but was whisked off to New York City when he was spotted by the producers of hit Broadway musical Finian's Rainbow.
The actor subsequently moved to Hollywood and landed roles in 22 movies, including 1953's The Desert Rats with Richard Burton, The Wreck of the Mary Deare in 1959 with Gary Cooper and Charlton Heston, and 1968's Star! with Julie Andrews.
Davis also appeared on more than 100 TV shows throughout his career, including The Twilight Zone, Perry Mason, and Alfred Hitchcock Presents, as well as clocking up more than 1,000 appearances on Broadway.
In the 1950s he became co-owner of the Hollywood School of Drama and The Hollywood Repertory Theater with actor Dan O'Herlihy, and later went on to expand his resume with roles as a writer, director and film producer. He wrote and directed films including Kennedy's Ireland, Thunder Run and The Violent Ones, before he quit the movie business in 1984 to run for Congress, winning the Democratic primary but losing the general election.
In his later years, Davis taught acting classes at the Actors and Singers Studio in Thousand Oaks, which he co-founded with his daughter, singer/actress Maripat Davis.
Davis is survived by his wife of 59 years, actress Marilyn O'Connor, his daughter and a son.