Danielsson was born in Krokek, Sweden and was the son of chief physician Emmerik Danielsson and Greta, née Källgren. His father died in a traffic accident when he was six years old, and after that Danielsson grew up in Norrköping with his mother and aunt, who were women that encouraged his adventuring ambitions. He obtained a Doctor of Licentiate from Uppsala University in 1954 and a Doctor of Philosophy in anthropology in 1955. Danielsson was intendant at the Bishop Museum in Honolulu, Hawaii from 1952 to 1966. Danielsson was Swedish consul in French Polynesia from 1961 to 1978 and extra museum director of Sweden's National Museum of Ethnology from 1966 to 1971. He was also correspondent for the Pacific Islands Monthly. He participated in the Swedish-Finish Amazon Expedition 1946-47, the Kon-Tiki expedition in 1947, Tuamotu Expedition 1949-51, the Pacific Science Board Expedition in 1952, Expedition to western Polynesia in 1953, Around Australia 1955-56, Vanderbilt Foundation expedition to the Society Islands in 1957 and Sveriges Radio's TV expedition to the South Pacific Ocean in 1962. After the Kon-Tiki expedition, Danielsson married in Lima in 1948, a French woman, Marie-Thérèse Sailley, daughter of factory owner Abel Sailley and Josephine, née Mayer. They decided to settle in Raroia, the atoll on which the raft had made landfall. They stayed there from 1949 to 1952, and in 1953 they moved to Tahiti. His doctoral thesis on the Tuamotusisland chain, submitted to Uppsala University in 1955, was published the following year as Work and Life on Raroia. He subsequently wrote many books and scripted many films, becoming one of the world's foremost students of Polynesia. He and his wife were particularly outspoken critics of French nuclear tests at Moruroa and Fangataufa atolls, and of the destruction of Polynesian culture through colonialism. Their daughter Maruia died from cancer. Marie-Thérèse and Bengt Danielsson received the Right Livelihood Award for their campaigning work in 1991. Bengt died in July 1997 following a deterioration in his health, and was buried at Östra Tollstad Church inMjölby Municipality, Sweden.
