Green-Ellis signed a three-year deal with the Bengals, ending his time with New England.
An undrafted rookie out of Ole Miss in 2008, Green-Ellis worked his way from the practice squad to contributor to starter, becoming the first Patriots player to record a 1,000-yard season since the days of Corey Dillon, when he totaled 1,008 in 2010.
Last year, Green-Ellis was again New England's leading rusher, though the rise of rookie Stevan Ridley and the Patriots' pass-happy offense meant he had just 181 carries. Green-Ellis had 667 yards and 11 touchdowns; over the last two years, he totaled 24 regular-season touchdowns.
Green-Ellis finishes his Patriots career with 547 total regular-season and postseason carries and zero fumbles.
Though Ridley, Danny Woodhead, and Shane Vereen remain on the New England roster, the team likely will pursue one of the many free agents still available at the position.
He came to the Patriots last year looking to reclaim a once-promising career, and collected 10 sacks in a part-time role, though several of his early-season sacks came in late-game situations when the Patriots had the game in hand.
Anderson garnered quite a bit of attention on the open market, visiting the Dolphins and Ravens in addition to Buffalo.
The Patriots would have welcomed both Green-Ellis and Anderson back, but the understanding all along was that it would be at a price the team wanted to pay. The numbers aren't out on Green-Ellis's deal yet, but it's safe to say New England wasn't going to pay Anderson what the Bills did.