Edmonds was the son of Reverend Henry Edmonds, who founded Independent Presbyterian Church in 1915, and Mary Edmonds. He attended South Highland Grammar School and graduated from Phillips High School before entering the Virginia Military Institute. While there he managed the college yearbook and served as president of the Glee Club. He graduated in 1948 with a degree in civil engineering.
Prior to completing his degree he was commissioned to the Corps of Engineers and did work in both the European and Pacific theaters during World War II. After graduation he served as a commander of an Engineer Aviation Battalion.
In 1952 Edmonds took a job at Rust Engineering, becoming a project manager in four years. He left for a while to work at Harbert Construction before returning to Rust, where he was promoted to chief engineer and then to vice-president. In 1967 he moved to Brussels, Belgium to head up Coppee Rust, the company's European affiliate and there was honored as "Knight of the Order of the Crown" by King Baudouin I of Belgium. He returned to Birmingham as Rust's Senior Vice-President for Operations in 1969.
In 1972 Edmonds joined two other Rust executives, Peter Bolvig and Ted C. Kennedy to form BE&K. Edmonds was the first president of the company and headed its engineering department. He became chairman in 1983, retiring in 1989.
Edmonds was named "Engineer of the Year" by the Alabama Society of Professional Engineers in 1983. He has been given an honorary Doctor of Science by UAB (1986) and was named "Citizen of the Year" by the Young Men's Business Club in 1988. He was inducted into the Alabama Academy of Honor in 1991, is a member of the Alabama Engineering Hall of Fame class of 1992 and was given the Distinguished Eagle Scout Award in 1996.
Edmonds continued serving on BE&K's board of directors during retirement and chaired the board of Kirkwood-by-the-River, a retirement community he founded along with his father. He also served on the boards of directors of the First Alabama Bank of Birmingham and Energen and as a trustee of the Southern Research Institute.
He was also a supporter of the Alabama Symphony Orchestra, serving as president of the Symphony Association and Chairman of the ASO Board of Directors. He was named the Alys Robinson Stephens Patron of the Arts in 2004. He was an active member and Elder at Independent Presbyterian Church.
- Goodman, Sherri C. (October 20, 2007) "BE&K co-founder Bill Edmonds dies." Birmingham News.
- Stanton, Al, et al. (1997) BE&K: The First 25 Years: A Work in Progress. Birmingham: BE&K.
- Edmonds bio at the Alabama Academy of Honor