Edmundson was the son of American Life Insurance Co. president Daniel Edmundson and his wife, Lorena. He attended the University of Alabama and served in New Guinea and the Philippine Islands during World War II as a 2nd lieutenant.
Edmundson founded the Southern Toy Co. with his brother, D. V. in 1946. He served as president and manager of the store while his brother resided in Ponte Vidra, Florida. He was married to the former Ruth Barrett and had four children: William Jr, Lee, Paul, and Lorena.
Edmundson was a member of the Birmingham Country Club and Vestavia Country Club. He suffered a heart attack while playing golf and died before reaching a hospital. He was interred in a family mausoleum at Elmwood Cemetery.
- "William Edmundson, founder of toy firm" obituary (June 2, 1958) The Birmingham News, p. 11