He was director of the Ethnographic Museum at the University of Oslo and as major contributor to Circumpolar studies.
He was the son of parish priest Marcus Jacob Gjessing (1871–1947) and Julie Kathrine Monrad (1877–1951).
He attended the University of Oslo where he received his Master's degree in archeology in 1931 and defended his doctoral dissertation in 1934.
He was an honorary member of the Royal Anthropological Institute of Great Britain and Ireland.
He was awarded the Fridtjof Nansen Prize for Outstanding Research and the Qvigstad Medal.