Wilfork, 33, won two Super Bowls with the Patriots and made five Pro Bowls from 2004 to 2014. He was also named a first-team All-Pro in 2012.
Last season, Wilfork appeared in 16 regular-season games and recorded 47 tackles and one interception for the Super Bowl XLIX champions.
Brady's post mirrors a statement from Patriots head coach Bill Belichick on Monday:
"Few players reached or will ever reach the special level of Vince Wilfork. He is a great champion and one of the classiest people I have ever been around—just a kind, genuine and giving person who was all about our team, football, winning and bringing joy to others. There may have never been anyone at his position with as much strength, toughness, intelligence, instinctiveness and athleticism. He is the best defensive linemen I ever coached, an all-time great Patriot whose place on our team will be missed but whose remarkable career as a Patriot will be remembered forever."
- Mike Fiammetta