Greene was the son of a Boston banker based in Paris. He was an archaeologist and founding member of the Société Française de Photographie and of the Société Asiatique. His first trip to Egypt in the fall of 1853 produced more than two hundred waxed-paper negatives. In 1854 Greene returned to Egypt with permission to excavate at Deir-el-Bahari, where he cleared the temple of Ramses III, photographing his progress. His health was adversely affected by his extended visits in Egypt's climate, and he died in Cairo in 1856.