Greer played center for the Bearcats from 1995 through 1998. He was a four-year letterman who started 37 consecutive games. He was elected team captain as a senior in 1998, and was selected as an American Football Coaches Association (AFCA) All-American, First Team Hewlett-Packard All-American and First Team USA Football All-American. He was named Third Team Hewlett-Packard All-American and First Team Sigma Alpha Epsilon All-American in 1997.
He earned First Team All-Northwest Conference honors in 1997 and 1998. He was chosen Second Team All-NWC in 1996.
He helped Willamette achieve a combined record of 35-8-1 (.807) during his four seasons, including 13-1 in 1997 and 9-2 in 1996. Greer helped the Bearcats advance to the NAIA Division II Championship game in 1997 after reaching the NAIA quarterfinals in 1996.
At the conclusion of his Willamette career he was selected to play for the NCAA Division III All-Star Team that defeated the Mexico All-Stars, 40-13. Later, he played one season in the European Pro Football Federation for the Paris Molasses, who won the Northern Division championship and placed second overall.