The kicker's two-year deal was agreed just a day before he was scheduled to become an unrestricted free agent.
He is already the Colts' all-time leader in points scored, extra points made and field goals made.
And he is one of only three kickers in the history of American football to have passed 500 career field goals.
Vinatieri's 48-yard kick to win Super Bowl XXXVI in 2002 is often credited as the moment that launched a period of New England Patriots dominance that saw them win the championship twice more in the next three seasons and reach six Super Bowls in 13 years.
American football
Only two other players have ever gone on to feature in pro football beyond the age of 45. Morten Anderson was 47 when he played his final game for the Atlanta Falcons in 2007, while quarterback George Blanda was 48 when he made his last outing for the Oakland Raiders in 1975.
Football
Salvador Reyes helped Mexican club Chivas to seven league titles in the 1950s and '60s. Arguably their greatest ever player, the club legend was honoured in later years when named in the starting line-up for a game against Pumas in 2008 - at the age of 71. He kicked off, took a return pass, played a neat one-two and kicked the ball into touch so he could be substituted.
Boxing
The WBC light-welterweight world champion from 1980-82, Saoul Mamby, made a comeback aged 60 - 26 years after holding that title. He fought in an officially sanctioned bout in the Cayman Islands in 2008, but lost in 10 rounds.
Cricket
Yorkshire and England all-rounder Wilfred Rhodes played his final Test for his country at the age of 52. He took four for 44 in the second innings against Australia as England won the 1930 Ashes.
Snooker
Three-time world champion Fred Davis won the British Boys Under-Six Billiards Championship in 1929 and only retired in 1993, aged 79, due to severe arthritis in his left knee.
Tennis
Martina Navratilova's mixed doubles win at the 2006 US Open came a month short of her 50th birthday and 32 years after her first Grand Slam title in 1974.
The NFL's oldest player, 43-year-old Adam Vinatieri, has signed a new deal with the Indianapolis Colts that will take him beyond his 45th birthday.