Nelson, who spent a brief period at MGM in the early 1940s before entering the U.S. Army, made his Broadway debut in 1943 in the wartime play Winged Victory. He returned to the Great White Way in 1948 to star in Moss Hart's Light Up the Sky.
His many other Broadway credits included The Rat Race, The Moon is Blue, Mary, Mary (a role he repeated on film opposite Debbie Reynolds), Cactus Flower, Seascape, and The Norman Conquests. In 1977, he starred opposite Liza Minnelli in the Kander-and-Ebb musical The Act, for which he received a Tony Award nomination for Best Actor in a Musical. His final Broadway appearance was as Julian Marsh in 42nd Street.
Nelson worked steadily in film and television for nearly 50 years. He was the first actor to play James Bond, appearing in a one-hour television of Casino Royale, and also appeared in Airport and The Shining.
He is survived by his wife, Nansi.