Jeff McLane of the Philadelphia Inquirer first reported the news.
The Patriots will send a 2020 fifth-round pick to Philly for Bennett and a 2020 seventh-round selection, Rapoport reported, per a source informed of the terms. The trade was finalized on March 14.
The Eagles had been shopping Bennett this week in an effort to clear cap space and recoup compensation in a market devoid of pass-rushing help.
Bennett is set to earn $7.2 million in 2019 and $8 million in 2020.
The 33-year-old told NFL Network's Good Morning Football on Friday morning he was not interested in a pay cut and instead wanted a pay raise. The comments precipitated the afternoon trade.
Though the Patriots aren't known to acquiesce to salary demands, especially from an aging veteran, trading for a still productive player at a reasonable salary is a very Belichickian move.
With pass rusher Trey Flowers heading to the free agent market, and looking like he'll garner a huge payday, New England immediately helps fill the potential void with a pass rusher that has proven he can still disrupt the quarterback.
"The family, everything is just, I've been so stationary and all of the sudden it's just like, I feel nomadic. I feel like the Berber tribe in Morocco: I'm pitching tent anywhere," Bennett said of the pending trade, per The Change-Up. "I feel it's an iconic person I get to play with, Tom Brady, and the rest of the organization. So I guess I can look forward to that, it's just a little bit different. I wasn't, I don't really know if I was really ready for all of that."
In his first year with the Eagles, Bennett tallied nine sacks and 34 tackles. Pro Football Focus charted Bennett with 22 QB hits and 44 pressures, including playoffs.
Despite his age, Bennett's ability to pester the passer remains intact, and his versatility to play up-and-down the D-line meshes well with Bill Belichick's defensive blueprint.