He was born in Collon in County Louth to farmer William Pomeroy Greene and Anne Griffith.
In 1842 the family moved to Melbourne, where William Greene established the Woodlands estate.
Greene studied at the University of Melbourne, where he received a Bachelor of Arts, and was subsequently a pastoralist on the Murray River.
On his return Greene bought Iandra, a 32,600 acre (13,193 ha) estate near Grenfell, in 1878 and began grazing and wheat-growing.
[1] In 1889 he was elected to the New South Wales Legislative Assembly as the Free Trade member for Grenfell.