Born in New York City, Nelson studied at the High School of the Performing Arts and began his career off-Broadway in 1955.
His many credits include Coco, The Magic Show, So Long, 174th Street, The Lady From Dubuque, The Tap Dance Kid, Sunday in the Park with George, Into the Woods, and revivals of Morning's at Seven, Awake and Sing!, Long Day's Journey Into Night, Blithe Spirit, The Night of the Iguana, and Private Lives, among others.
He also designed the lighting for the Ronald Reagan Memorial Library in Simi Valley, California.
In addition to his theatre work, Nelson helped define the use of light as an important element in modern dance.
He worked with such choreographers as Martha Graham, Paul Taylor, Twyla Tharp and Erick Hawkins.