Belichick and Kraft mutually agreed to part ways after the team finished the season with a dismal 4-13 record, the worst in Belichick's 29-year head coaching career.
"I'll always be a Patriot," Belichick said at a press conference where he maintained his famously stoic demeanour.
"I look forward to coming back here but at this time we're going to move on.
"I look forward and am excited for the future but will always be very appreciative of the opportunity here, the support here, and for what Robert has done for me."
Belichick also thanked the more than 1,000 players he coached during his tenure in New England as well as the team's staff, fans and media.
Kraft said it was an emotional day for him and the Patriots fanbase but emphasized that the decision was mutual and amicable.
"The man standing to my left brought the leadership and coaching skills that were needed to make the type of unprecedented success we had possible," Kraft said at the press conference.
"Coach Belichick will forever be celebrated as a legendary sports icon here in New England and I believe will go in as a Pro Football Hall of Famer on the first ballot.
"Why? Because he is the greatest coach of all time... what he has accomplished with us will never be replicated."
With six Super Bowl titles in 24 seasons with the Patriots, Belichick is regarded as one of the greatest coaches of all time, leading the most decorated NFL dynasty in league history.
Speculation has mounted since November, however, that the New England team was ready for a coaching change as they grappled with their third losing season in four years since quarterback Tom Brady left to play for the Tampa Bay Buccaneers in 2020.
Appointed head coach in 2000, he led the Patriots to a 266-121 record, 17 AFC East titles - including a league-record streak of 11 in a row from 2009 - and the team's nine Super Bowl appearances are tied for most by an NFL franchise. Their last Super Bowl victory was in 2018.
Belichick has more Super Bowl appearances as head coach than any team has made in NFL history, except the Patriots (with 11), and his 17 division titles are the most by a head coach with a single club.
Belichick's departure comes a day after Nick Saban retired after 17 seasons as head coach at Alabama and longtime Seattle Seahawks head coach Pete Carroll moved to an advisory position.
