Hassell, who was born in the Norwegian capital of Christiania (now Oslo), was educated at the university there and in Berlin where he obtained his doctorate in 1924. He immediately returned to the University of Oslo and served there as professor of chemistry from 1934 until his retirement in 1964.

Early in his career, following studies on how organic dyes photosensitize silver halides, Hassell discovered adsorption indicators. In 1943 he published an important conformational analysis of cyclohexane but, as he refused to use the language of the German conquerors and published it in Norwegian, its influence was considerably reduced. The molecule exists in two main forms, the so-called boat and chair conformations; Hassell was able to show the chair form to be the most stable. It was for his work on conformation that he shared the 1969 Nobel Prize for chemistry with Derek Barton.