Rosenstein was born in Uppsala, Sweden. He was the son of professor Samuel Aurivillius and Anna Margaretha Rosén von Rosenstein. He belonged to the Swedish nobility. The "von Rosenstein" surname was his mother's family name which came through an adoption. His maternal grandfather was Uppsala University professor of medicine Nils Rosén von Rosenstein (1706–1773).[2]
He attended Uppsala University where he first studied classical literature followed by theology. In 1786, at the age of 20, Rosenstein defended his PhD. He was ordained a priest in 1791 after becoming master of primus and associate professor of theology in 1790. In 1792 he became theology liceniat. He served as a theology lecturer at the University of Uppsala, leaving in 1796 to become pastor in the pastorate of Kumla and Hallsberg. In 1809, he was appointed Bishop of the Diocese of Linköping and in 1819 Archbishop of Uppsala.
He was also a member of the Royal Swedish Academy of Sciences from 1809 and of the Swedish Academy from 1819.
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