Gostkowski was drafted by the New England Patriots in the fourth round of the 2006 NFL Draft with the 118th overall pick. He was the first of two placekickers to be selected that year. During the Patriots' 2006 training camp, he competed with veteran kicker Martín Gramática, who the Patriots had signed as a free agent after Adam Vinatieri signed with the Indianapolis Colts. On August 23, 2006, before their third preseason game, the Patriots cut Gramática, and gave the job to rookie Gostkowski.