Vinatieri has played the last 12 seasons with the Colts. He previous contract expired after the 2017 campaign, which had made him eligible for free agency when the new league year begins on March 14.
The 45-year-old spent the first 10 seasons of his career with New England, and connected on game-winning field goals in each of the Patriots' first two Super Bowl wins -- in 2001 versus the then-St. Louis Rams and 2003 against the Carolina Panthers.
Vinatieri has kicked 559 field goals during his career, which puts him just six shy of Hall of Famer Morten Andersen for the most in NFL history. His 2,487 points trail only Andersen (2,544) in league history to boot.
A three-time Pro Bowl selection, Vinatieri connected on 29 of 34 field-goal attempts last season, including five of six from at least 50 yards out. Two of his misses last season came during blizzard conditions in Buffalo.
Vinatieri has recorded at least 100 points in each of his past six seasons.