Greenberg, the son of Conservative Jewish parents, was raised in Columbus, Ohio. When he was about 15, he began studying with an rabbi. He attended Yeshiva University in New York as an undergraduate and then as a rabbinical student. When he was 20, he went to study at the Yeshivat Har Etzion, a hesder yeshiva in Alon Shvut in Gush Etzion near Jerusalem. He received his BA in philosophy from Yeshiva University, and his rabbinic ordination from the rabbinical seminary of Yeshiva University (RIETS) in 1983.