Fossum was born in Cherry Hill, New Jersey. He attended Midway High School in Waco, Texas. He then attended Texas A&M University, leading the Aggies to the 1999 College World Series in Omaha, Nebraska. He earned All-Big 12 honors in both 1998 and 1999, highlighted by a 12–7 record and 3.64 earned run average (ERA) during his junior campaign, establishing a single-season school mark with 162 strikeouts. Fossum also won the C. E. "Pat" Olsen Outstanding Pitcher Award in 1999 and was a second team All-American in 1998.