Thorsby introduced tissue typing and transplant immunology as a field of study in Norwegian medicine, used for identifying tissue type–compatible donors and recipients in transplants. He was also involved in launching Scandiatransplant, the Nordic cooperation organization for organ transplants. He worked at Ullevål University Hospital and Oslo University Hospital. He established the Tissue Type Laboratory at Oslo University Hospital in 1970, which later became the Department of Transplant Immunology. Thorsby was the head of the department from 1970 to 1998. In 1983 he became a professor at the University of Oslo. He was also the chief physician at the Department of Immunology, where he was the head of department from 1998 to 2006. From 1989 to 1990 he was dean of the University of Oslo Faculty of Medicine. Thorsby became the president of the European Federation for Immunogenetics in 2002.
