David was the CIF champion and Player of the Year at Verbum Dei High School, as a dominating 6-9 center when his team won 39 straight games. He went to UCLA (1976-79) to become a two-time College All-American and two-time Pac-10 Player of the Year when he led the Bruins in scoring and rebounds, with a NCAA Final Four appearance. He finished his career averaging 15 points and 9 rebounds per game, while shooting 54% from the floor (UCLA was 102-17, .857 winning percentage).

He was the 2nd overall pick of the 1979 NBA Draft (behind Magic Johnson) with the Chicago Bulls, and had a successful 12-year pro career, including making the All-Rookie Team. His professional team highlight was being part of the 1990 NBA championship Detroit Pistons squad. He retired from the NBA in 1991, after playing in 823 games. He was the head coach at Verbum Dei for two years, winning the California State Division IV titles in both 1998 and 1999, with a 54-12 record. Greenwood was inducted into the UCLA Athletics Hall of Fame in 1997, and the College Basketball Hall of Fame in 2021.