 Greenaway was on the varsity baseball team at the Bronx High School of Science, from which he graduated in 1974.Greenaway earned a Bachelors of Arts degree from Columbia University in 1978 and a Juris Doctor from Harvard Law School in 1981.From 1982 until 1983, he worked as a law clerk for Judge Vincent Lyons Broderick of the United States District Court for the Southern District of New York.