The sides had faced a 4 p.m. ET deadline to reach a multiyear contract after the Patriots had designated Gostkowski as its franchise player in early March.
Gostkowski, who has played his entire career with the Patriots after being selected in the fourth round of the 2006 draft as the replacement for Adam Vinatieri, was the NFL's leading scorer in 2014 with 156 points.
A Pro Bowler in each of the last two seasons, he has one of the strongest legs in the NFL, which the Patriots, as a team based in the Northeast often playing in adverse conditions, have valued. Gostkowski's strong leg was reflected in his 53 touchbacks during the 2014 regular season, which tied for fifth most in the league.
The 31-year-old Gostkowski was 35-of-37 on field goals in 2014, hitting all 51 extra points that he attempted. He became New England's all-time leading scorer in 2014, passing Vinatieri.
ESPN NFL Insider Adam Schefter contributed to this report.