Green was born in Victoria, British Columbia in 1876 to Alexander Alfred Green and Theophila Turner Raines. After the death of his father in 1891, Green relocated to Montreal to attend McGill University where he would obtain his medical degree.
He attended Corrig College at Victoria.
Upon his graduation from McGill in 1898, Green worked as a physician on the construction of the Canadian Pacific Railway Crowsnest Pass line, in the Kootenay Valley, working on horseback. During the time he operated a hospital and treated many during an epidemic of typhoid. He later settled at Cranbrook, British Columbia, in the Kootenay Valley in 1899 to establish a medical practice.
He was one of the first and only physicians, a medical pioneer at Cranbrook.
In the British Columbia general election, 1941, Green was elected as a Conservative to the Legislative Assembly of British Columbia for the district of Cranbrook. He was elected again in 1945 as a coalition member, serving until his retirement in 1949.
Frank West. Green died in 1953 of heart problems at Saint Eugene Hospital in Cranbrook, which he had established. He was later cremated in Calgary.
The F. West. Green Medical Centre and F. West. Green Memorial Home continuing care centre at Cranbrook are both named after him.
