Paterson was born in Edinburgh and served in the First World War, where he won the MC. After the war he studied medicine at Edinburgh University, graduating in 1923, and took the MD in 1927. He began to study radiology, receiving the DMRE in 1924, and researching the subject at the Mayo Clinic and at the University of Chicago. In 1930 he was appointed Acting Director of the Radiological Department at Edinburgh Royal Infirmary. Soon after he became director of radiotherapy at the Christie Hospital and Holt Radium Institute, Manchester, at a time when these two institutions had merged and were reopening at a new site.
Paterson's played a major role in building an international reputation for the Christie Hospital through developing its radiological services. He created, with H.P. Parker, the Paterson-Parker rule for radium therapy, a reliable guide to safe dosimetry. He also under with his researchers, a new method for treating cancer of the uterine cervix. Paterson introduced statistical study to help evaluate treatments provided, and detailed statistical reports were produced about Christie patients in 1939, 1946 and 1950. Paterson also had considerable skills as a medical administrator, planning a fully equipped radiotherapy centre, backed by a network of peripheral consultation and follow-up clinics. This model was eventually adopted on a national level. Paterson also stressed the importance of educating the public about cancer and helped establish the Manchester Regional Committee for Cancer Education. In 1947, Paterson started trials to investigate the success of radiation therapy for breast cancer.
Paterson held many professional appointments: hew as president of the British Association of Radiotherapists in 1938-9, president of the Faculty of Radiotherapists and president of the International Radiological Congress in 1949. He was a member of the Grand Council and Scientific Committee of the British Empire Cancer Campaign. From 1960-2 he was professor of radiotherapeutics at the University of Manchester. He was appointed CBE in 1950.