Gostkowski attended the University of Memphis, where he played for the Memphis Tigers football team and majored in exercise and sports science. Gostkowski received an athletic scholarship to play baseball for Memphis, and was a walk-on for the football team. He finished his college career with a total of 369 points, a school record, and 13th overall in NCAA Division I-A history, converting 70 of 92 field goals and 159 of 165 extra points (PATs) during his Tiger career. His 70 field goals and 159 extra points both set school records previously held by Joe Allison (1990–1993). He earned first team All-Conference USA honors in both his junior and senior years and was named Conference USA's Special Teams Player of the Year in 2005.