In 1975, he was appointed to the Nobel Foundation Board of Directors in Sweden,[2] and was awarded the Louisa Gross Horwitz Prize from Columbia University, together with Bengt I. Samuelsson.

He shared the Nobel Prize in Physiology or Medicine with Bengt I. Samuelsson and John R. Vane in 1982, for discoveries concerning prostaglandins and related substances.

Bergström was elected a member of the Royal Swedish Academy of Sciences in 1965, and its President in 1983.

[3] He was also a member of both the United States National Academy of Sciences and the American Philosophical Society.

[8] He had two sons, the businessman Rurik Reenstierna, with Maj Gernandt; and the evolutionary geneticist Svante Pääbo (winner of the 2022 Nobel Prize in Physiology or Medicine), from an extramarital affair with Karin Pääbo, an Estonian chemist.