Tabori is the son of director Don Siegal and Swedish-American actress Viveca Lindfors. He appeared in one of his mother's films, Weddings and Babies, as a young boy. His parents divorced in 1953 and Lindfors married Hungarian writer and director George Tabori. He adopted his stepfather's surname and changed the English spelling of his forename.
He started his career as a stage actor in his teens in the late 1960s, and during the 1970s and 1980s he appeared in many films, including Arthur Miller's A Memory of Two Mondays. In 1988 he played the part of Sir Henry Baskerville in The Hound of the Baskervilles next to Jeremy Brett as Sherlock Holmes and Edward Hardwicke as Dr. Watson. In 1989, he played Professor Peter Plum in the first television series of Cluedo, where he was known for his loud protestations of innocence during the studio-based portions of the program.
During the 1990s, Tabori began directing in television. He also voiced HK-47, the assassin droid and comic relief character in the video games Star Wars: Knights of the Old Republic and Star Wars: Knights of the Old Republic II: The Sith Lords, as well as providing the voices for some characters in other Star Wars related products and in the Battlestar Galactica area. Tabori was also featured on the radio program CBS Radio Mystery Theatre.