Greene was the son of Rinaldo and Martha Bullard Greene of Opelika. He was educated in the common schools there and went on to earn a bachelor of arts at Emory College in Oxford, Georgia in 1884. In 1886 he completed a bachelor of laws degree at the University of Alabama School of Law and began practicing in Birmingham.
On May 6, 1896 Greene married the former Margaret Jordan Morrow, daughter of George and Marry Ella Morrow and granddaughter of Hugh Morrow and James Smith. They had two daughters, Mary George and Susie Morrow.
Greene was elected to the legislature that same year and served one two-year term. In 1900 he was elected an associate criminal court judge for the 10th Judicial Circuit of Alabama and served until 1910.
- Dubose, Joel Campbell (1904) Notable men of Alabama: Personal and Genealogical 2 Volumes. Atlanta, Georgia: Southern Historical Association