The actor’s publicist, Dick Guttman said: “We are overcome with sadness”.
The ‘Cleopatra’ star died on Saturday in Los Angeles of “unexpected complications” following a hospital visit.
His career spanned six decades, but he was best known for playing master of disguise Rollin Hand in the 1960s television series, ‘Mission:Impossible’.
He famously turned down the role of Mr Spock in ‘Star Trek’, which went to his close friend Leonard Nimoy instead.
The ‘Star Trek’ actor later replaced him on ‘Mission: Impossible’, when Landau left following a dispute over pay.
His first big movie role was in Alfred Hitchcock’s ‘North by Northwest’, and he also starred in ‘Cleopatra’ and numerous TV shows, including ‘The Twilight Zone’ and ‘Buffalo Bill’.
During his career he was nominated for three Academy Awards for Best Supporting Actor, for playing Abe Karatz in Francis Coppola’s ‘Tucker’ in 1988, and as Judah Rosenthal in Woody Allen’s ‘Crimes and Misdemeanors’ in 1989.
He eventually won for his role as the horror movie star Bela Lugosi in Tim Burton’s ‘Ed Wood’ in 1994.