Gossett attended the University of Texas, and was a two-time first-team All-American member of the golf team. He won the U.S. Amateur, the Big 12 Championship, and was the Big 12 Student-Athlete of the Year in 1999. He was also a member of the Walker Cup team in 1999. He turned pro in 2000. Gossett won his first official PGA Tour event in 2001 at the John Deere Classic.