The NFL Network's Ian Rapaport adds that Butler's deal is for five years and $61 million, $30 million of which is guaranteed.
Butler will be reunited with two former Patriots in former linebacker Mike Vrabel and personnel man Jon Robinson. Last season Lewis posted 896 yards and six touchdowns on the ground with 214 yards and three touchdowns receiving.
He intercepted Russell Wilson's pass at the goal line with 20 seconds left in the game, preventing a go-ahead touchdown from the Seattle Seahawks. New England almost traded him to the New Orleans Saints last offseason for Brandin Cooks, but that deal fell apart.
Butler had another strong season in 2016, but did not receive a contract extension from the team and instead became a restricted free agent. After a slow start, he ended up playing 98 percent of New England's defensive snaps and finished the season with two interceptions.
The New Orleans Saints pursued Butler as a restricted free agent a year ago, but the trade price was too high.
General manager Jon Robinson, hired in January 2016, got his National Football League start as a New England scout.
Malcolm Butler is officially moving on from the Patriots. There's another $3 million via incentives.
Despite Butler's sudden stardom, Belichick said at one point in 2015 that Butler "as much as any player that I've been around, has really not changed very much from Year 1 to Year 2". He had nine carries for 39 yards in the Patriots' 41-33 loss to the Eagles in Super Bowl LII. Butler is not coming off a career year, but he's played well in recent seasons despite often following top opposing receivers.