Greene was the son of Robert N. and Sarah Earle Greene, both natives of Jefferson County from pioneer families. He grew up on the Earle-Greene plantation and was educated in Elyton and Jefferson County Schools and earned his undergraduate degree at Washington and Lee University in Lexington, Virginia. He returned to Elyton and Birmingham to teach and read law and, once admitted to the bar, opened a practice in 1880 in Jasper.
Greene returned to Birmingham in 1883 and was elected to the Alabama House of Representatives in 1884, serving two years. In 1887 Governor Thomas Seay appointed him criminal court judge for Jefferson County, filling a vacancy. He was elected to the same position in 1888 for a six-year term, and re-elected continuously for over 30 years.
- Dubose, Joel Campbell (1904) Notable men of Alabama: Personal and Genealogical Vol. 1. Atlanta, Georgia: Southern Historical Association