Donnelly was born in Glasgow in 1936, graduated from St Mary's Hospital Medical School in 1961 and became a Fellow of the Royal College of Surgeons in Edinburgh in 1969.
In 1973, he was a research fellow at Massachusetts General Hospital, and in 1975 was appointed a Consultant in Liverpool specialising in paediatric cardiac and adult thoracic surgery.
He served on the National Executive of the Society of Thoracic and Cardiovascular Surgeons of Great Britain and Ireland and was chairman of the Medical Research Council Working Party on cancer of the oesophagus.
[2] In 1990 Donnelly founded the Lung Cancer Fund to promote an intensive research programme into the causes, prevention and management of the disease.
[5] In 1997, he opened a new Roy Castle Lung Cancer Foundation office in his home town of Glasgow, to provide patient information and support.