Davoren was born in Campsie, New South Wales, and was educated at Sydney Technical High School. He was a senior production planner with the State Rail Authority and director of a co-operative building society and credit union before entering politics. He was president of the Punchbowl branch of the Australian Labor Party 1970–84 and secretary of the Lakemba State Electoral Committee 1965–84.
In 1984, the Labor member for Lakemba, Vince Durick, retired and Davoren was selected as his replacement. He won the seat easily, but was only narrowly successful in 1988. Davoren retired in 1995, the seat going to Tony Stewart.
Davoren died on 21 September 2010 at the age of 82.
- "Mr (Wes) Westby James DAVOREN (1928 - 2010)". Parliament of New South Wales. 2010. http://www.parliament.nsw.gov.au/prod/parlment/members.nsf/1fb6ebed995667c2ca256ea100825164/082a0f01a500b730ca256a94001c063a?OpenDocument.
- Green, Antony (2010). "Elections for the District of - Lakemba". Parliament of New South Wales. http://www.parliament.nsw.gov.au/resources/nswelectionsanalysis/DistrictIndexes/Lakemba.htm.
- "Former NSW Labor MP Davoren dies". The Sydney Morning Herald. September 22, 2010. http://news.smh.com.au/breaking-news-national/former-nsw-labor-mp-davoren-dies-20100922-15muc.html.