Fehn was born at Kongsberg in Buskerud, Norway. He was the son of John Tryggve Fehn (1894–1981) and Sigrid Johnsen (1895–1985). He received his architectural education at the Oslo School of Architecture and Design in Oslo. He entered his course of study in 1946 and graduated during 1949. Among other instructors, he studied under Arne Korsmo (1900–1968).

In 1949, Fehn and architect Geir Grung (1926–1989) won the competition for the Museum Building for the Sandvig Collections at Maihaugen in Lillehammer. In 1950, Fehn joined PAGON (Progressive Architects Group Oslo, Norway). The group, which was led by Arne Korsmo, had the goal of implementing and promoting modern architecture.

In 1952, he married Ingrid Løvberg Pettersen (1929–2005). Fehn died in his Oslo home at the age of 84. He was survived by his son Guy Fehn and four grandchildren.

In 1952–1953, during travels in Morocco, he discovered vernacular architecture, which was to deeply influence his future work. Later he moved to Paris, where he worked for two years in the studio of Jean Prouvé, and where he knew Le Corbusier. On his return to Norway in 1954, he opened a studio of his own in Oslo.

In 1961, he was awarded the Houen Foundation Award, jointly with Geir Grung, for the design of the Økern Nursing Home in Oslo. He received the Houen Foundation Award for his design of the Hedmark Museum at Hamar in 1975. In 1994 he was appointed Commander in the Order of St. Olav.

His highest international honour came in 1997, when he was awarded both the Pritzker Architecture Prize and the Heinrich Tessenow Gold Medal (Heinrich-Tessenow-Medaille).

In 1998, he was awarded the Norsk kulturråds ærespris. Sverre Fehn was awarded the first Grosch medal in 2001. In 2003, he was awarded the Anders Jahre Cultural Prize (Anders Jahres kulturpris).