Strömholm received his education in Uppsala (B.A. 1952; LL.B. 1957, Licentiate 1957). He completed a doctorate in Law in Uppsala in 1966. He was Professor in Jurisprudence in Uppsala from 1969, and Professor in Private Law and Conflict of Laws there 1982-1997. After an appointment as prorector (deputy vice-chancellor) of Uppsala University 1978-1989, he was rector magnificus (vice-chancellor) of the university 1989-1997. On June 5, 1992 Strömholm received an honorary doctorate from the Faculty of Humanities at Uppsala University, Sweden. 
On his retirement from the rectorial chair in 1997, he received a festschrift, Festskrift till Stig Strömholm (Uppsala 1997), in two volumes and 925 pages, including a partial bibliography (ISBN 91-7678-341-3).
- "Priser og utmerkelser" (in Norwegian). Royal Norwegian Society of Sciences and Letters. Retrieved 7 June 2007.
- "Gruppe 6: Rettsvitenskap" (in Norwegian). Norwegian Academy of Science and Letters. Retrieved 25 December 2010.
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