MB ChB Manch 1895, MD 1900, BSc 1908; LRCP LRCS Edin, LRFPS Glasgow 1895; DPH RCPSI 1897.
Greenwood studied medicine at the University of Manchester and Owens College and in 1895 he was appointed clinical assistant to the Cancer Hospital and Pavilion (later Christie Hospital Manchester). He was medical officer to Manchester Children's Hospital, assistant to the Public Health Laboratories in Manchester and medical officer of health for Blackburn and Crewe. Greenwood was later appointed medical officer of health and chief tuberculosis officer for Kent County Council. He was a fellow of the Society of Medical Officers of Health and was president of the North Western Branch.