Nelsen grew up in Nebraska and in Medford, Oregon. "He was a dust-bowl refugee," said Eric Nelsen. "He fled Ruskin and moved to Medford, Oregon -- just like in Steinbeck's Grapes of Wrath" (The Seattle Times). He came to Seattle in 1951, after service in the infantry in World War II's Pacific campaigns where he was awarded the Purple Heart and the Bronze Star. He received a degree in architecture from the University of Oregon. He moved to Seattle in 1951 and opened an architecture office in the University District in 1953.
Along with colleagues Ralph Anderson (1924-2010), Victor Steinbrueck (1911-1985), furniture maker Masin Black, investor Alan Black, and developer Richard White, Nelsen was active in preserving landmarks in Seattle, including historic buildings in Pioneer Square and in the Pike Place Market.
He was president of Allied Arts and a chairman of the Seattle Arts Commission. He was also also a principal in less formal groups such as The Chowder Society, interested in the future of Seattle. Nelsen also worked part time as an associate professor of Architecture at the University of Washington from 1957 to 1965.
Other commissions include renovations to the headquarters for the Boy Scouts of America on Rainier Avenue, the Merrill Court Town Houses on Capitol Hill, the restoration of the Governor's Mansion in Olympia, and the home of artist Morris Graves in Loleta, California, "The Lake."
Nelsen died on July 19, 2001 after complications from prostate cancer.