Greene was born at the family home at the Fishmarket Pub, Spanish Arch.
His father was Coleman Greene of Carna and his mother was Julia McGrath from Newcastle.
He was a member of the Old Irish Republican Army from 1917 to 1926, when he joined Fianna Fáil.
As Mayor, he opened the first Galway Oyster Festival in September 1954.
It was formally presented to the Mayor by the Dutch Ambassador in the city's Great Southern Hotel.