Hassel was born in Kristiania (now Oslo), Norway. His parents were Ernst Hassel (1848–1905), a gynaecologist, and Mathilde Klaveness (1860–1955). In 1915, he entered the University of Oslo where he studied mathematics, physics and chemistry, and graduated in 1920. After taking a year off from studying, he went to Munich, Germany to work in the laboratory of Professor Kasimir Fajans. His work there led to the detection of absorption indicators. After moving to Berlin, he worked at the Kaiser Wilhelm Institute, where he began to do research on X-ray crystallography. He furthered his research with a Rockefeller Fellowship, obtained with the help of Fritz Haber. In 1924, he obtained his PhD from Humboldt University of Berlin, before moving to his alma mater, the University of Oslo, where he worked from 1925 through 1964. He became a professor in 1934.