He played college football at the University of Miami and attended Baldwin High School in Pittsburgh, Pennsylvania.

[1] Greaves was a three-year starter for the Miami Hurricanes ('56 -'58) and a multi-year, All American candidate who played both offensive and defensive tackle.

Up until this time, He was considered to be the most prolific defensive player in Hurricane history, breaking the school's all-time career tackling record during his Junior season.

[2] Greaves played offensive tackle for the AFL Houston Oilers team and was a participant in the 1960 American Football League Championship Game.

Greaves spent a single season with the Oilers, before leaving to serve in the United States Army during the Berlin Crisis.