Family friend Wendy Bleiweiss says Johnson died Friday at an assisted living center in Nyack, New York. He was 92.
Johnson was known for his boy-next-door wholesomeness and was a major heartthrob in the 1940s.
Among his films were "Brigadoon," "A Guy Named Joe" and "The Caine Mutiny." His co-stars included Humphrey Bogart, Elizabeth Taylor and June Allyson.
Many of his early films had World War II themes, including "30 Seconds Over Tokyo."