William Greenwood was born in Blackburn, Lancashire in 1877. After studying at Birmingham Technical School in Birmingham, England, he was articled to Angelo W. R. Simpson (1852-1935) and F. W. Duckworth of Simpson & Duckworth from 1893 to 1897. He then remained with them for a further year as clerk of works and as an assistant.
Greenwood qualified as an architect in 1902 and was awarded the Ashpitel Prize that year. In 1903 he was elected an Associate of the Royal Institute of British Architects (ARIBA).
Greenwood practised as an architect in Blackburn, Lancashire from c.1902. A photograph of the hall at 'Mireash', Mellor, near Blackburn, Lancashire, designed by Greenwood is illustrated in The Studio Yearbook of Decorative Art vol.21, 1926 (p.46).
Greenwood's address was given as 11 Richmond Terrace, Blackburn in 1938. He died in Blackburn in 1952
Directory of British Architects 1834-1914. Compiled by Antonia Brodie, et al. Volume 1: A-K. London; New York: British Architectural Library, Royal Institute of British Architects/Continuum, 2001
'Obituary'. RIBA Journal vol. 60, March 1953 p. 207