Carl Olof Werner Sundby was born at Karlskoga in Örebro County, Sweden. Sundby was ordained a priest in the Diocese of Karlstad in 1943. He became a doctor of theology in 1959. He was a parish priest in the parishes of St. Peter's Priory, Lund and Norra Nöbbelöv in Lund from 1960–1970. He was bishop of the Diocese of Växjö from 1970–1972 and archbishop of Uppsala 1972–1983. He was Chairman of the Swedish Ecumenical Committee 1972–1983, chaired the Lutheran World Federation Executive Council 1973-77 and served as President of the World Council of Churches 1975–1983.
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Sundby died during 1996 and was buried at Klosterkyrkogården in Lund.