Brady, who turns 43 this summer, will become an unrestricted free agent when free agency opens on Wednesday.
During his 20 seasons with the Patriots, Brady was coached by Bill Belichick and together the pair brought unprecedented levels of success to the team, reaching nine Super Bowls.
The 199th pick in the sixth round of the 2000 draft, Brady rose from relative anonymity to become one of the greatest NFL players of all time.
He has won three NFL Most Valuable Player awards and leaves the Patriots second in the NFL all-time list in passing touchdowns (541) and passing yards (74,571).
Since getting his first chance in 2001, courtesy of an injury to then starter Drew Bledsoe, Brady has gone on to break numerous records, including most Super Bowl victories by a player (six), most Super Bowl MVPs (four) and most regular-season wins by a starting quarterback (219).
Addressing teammates, coaching staff and Patriots executives, Brady said in Tuesday’s statement: “You all have allowed me to maximize my potential and that is all a player can hope for.
“Everything we have accomplished brings me great joy and the lessons I have learned will carry on with me forever.
“I couldn’t be the man I am today without the relationships you have allowed me to build with you.”
Brady, who will be on the open market for the first time in his long career, did not indicate which team he will sign with for the 2020 season.