David Sayler, a senior executive athletics director, had been serving as Rice's athletics director in the interim.
Greenspan was Indiana's AD from 2004-08. He resigned amid NCAA allegations that his department failed to monitor basketball coach Kelvin Sampson.
The NCAA ruled that Sampson committed five major rules violations. Greenspan asked for Sampson's resignation, imposed internal penalties on the program and hired Tom Crean to take over the team.
Greenspan previously worked as the AD at Illinois State (1993-99) and Army (1999-2004).
