Bennett will be packaged with a 2020 seventh-round pick, while the Eagles will get back a 2020 fifth-round pick, a source told ESPN's Adam Schefter.
The move comes hours after Bennett stated he wouldn't take a pay cut to stay with the Eagles and was actually looking for a raise. The Eagles were ready to move on from Bennett for salary-cap reasons.
Bennett, 33, will join the same franchise his younger brother, Martellus, won Super Bowl LI with in 2017. Michael Bennett played against the Patriots in Super Bowl XLIX, losing as a member of the Seattle Seahawks.
He posted 34 tackles and nine sacks in his lone campaign with the Eagles.
It's unclear whether his arrival signals that the Patriots expect to lose fellow defensive end Trey Flowers in free agency.
The trade can't become official until March 13, the first day of the new league year.