His father, also named Tommy Green, had a career as a footballer and had also played for West Bromwich Albion.
He signed for West Bromwich Albion as an amateur in October 1931 and turned professional in March 1932.
He transferred to West Ham United in December 1936, for a £3,000 fee, scoring six goals in 44 first-team appearances for the East London club.
After scoring twice in nine games for Coventry, he moved to Worcester City in 1941, before finishing his playing career at Bromyard F.C (1945–1949).
This biographical article related to association football in England, about a forward born in the 1910s, is a stub.