He attended school in Fredrikstad in Østfold county, Norway. He was educated at the Technical School in Örebro, Sweden and then at the Royal Saxon Polytechnicum (now Dresden University of Technology) in Dresden, Germany before emigrating to the United States in 1880.
Cappelen was initially employed by the Northern Pacific Railroad and in 1886 became a City of Minneapolis bridge engineer He was elected City Engineer in 1893 and re-elected in 1913. He held membership in the American Society of Municipal Improvements and the Minneapolis Society of Engineers.
Cappelen was responsible for the design of many public works buildings in Minneapolis, for example the Prospect Park Water Tower, the Kenwood Park Water Tower, and the Cappelen Memorial Bridge, which is named in honor of him.
Frederick William Cappelen died during the construction of the bridge, and as a memorial to his life and career, the bridge still bears his name.
He was elected a member of the American Society of Civil Engineers on April 3, 1895.