Green was born and went to primary school in Avoca, Victoria, but left school to work for a telephone company in Ballarat and later in the family's bricklaying business. He travelled in the United States and Central America between 1889 and 1895 and as a result was known as "Texas". In June 1895, he moved to Western Australia and established a branch of the Australian Natives Association (A.N.A.) in Perth. In November 1895, he became a postal clerk in the gold rush town of Coolgardie. He was soon transferred to nearby Kalgoorlie, where he founded branches of the A.N.A. and the Post and Telegraphists' Union and became involved in local Labour politics. He married Emily Elenor Berry in January 1899.
Green campaigned for a strong air force and was appointed Minister for Defence in the Scullin government in October 1929. Despite the onset of the Great Depression, he implemented a training scheme for Australian pilots and purchased several aircraft. He also abolished compulsory military service. In February 1931, following the resignation of Joseph Lyons, he was appointed Postmaster-General. He was upset by Lyons' defection from the Labor Party and, according to G. C. Bolton, Green chased Lyons's train along the Canberra railway station platform shouting "For God's sake, don't do it, Joe!" In opposition after the 1931 elections, he campaigned for fellow Western Australian, John Curtin to be elected party leader.
Green died at East Coolgardie, survived by his wife and three sons and a daughter.