Per ESPN's Paul Kuharsky, Matthews has signed a 3-year deal with the Tennessee Titans. It should be noted that the three wide receivers that the Patriots really wanted this free agency period have been Marvin Jones, Mohamed Sanu, and Matthews, and all three are linked to teams under the control of fomer Patriots staffers.
Jones landed in Detroit with the Lions, where general manager Bob Quinn just departed from being the Patriots director of pro scouting. Sanu is seriously linked to the Falcons, where former Patriots director of college scouting Thomas Dimitroff serves as general manager, and where former Patriots vice president of player personnel Scott Pioli is assistant general manager.
And now Matthews has landed in Tennessee where former Patriots director of college scouting Jon Robinson serves as general manager. That's the double-edged sword of spreading talent to other front offices- they'll end up wanting the same players, and the bad teams will have more to offer.
Matthews wanted to have the chance to be a #1 receiver, with a minimum of being a #2 receiver, so he narrowed his options to the Patriots and the Titans.
The Patriots have tight end Rob Gronkowski, while the Titans have Delanie Walker, so that position is essentially a draw from a target-distribution perspective.
At wide receiver, New England has a #1 in Julian Edelman, with Danny Amendola playing in the slot and competing to be the #2 option. Matthews would be the priority outside receiver, but his path towards being a #1 is blocked by Edelman- and Edelman's cheap contract likely meant that his contract offer to the Patriots was less than what the Titans were able to offer.
The Titans don't have a clear-cut #1 wide receiver. Kendall Wright is entering the final season of his contract and was injured and semi-phased out of the offense last season. Justin Hunter is also entering the final season of his contract and he's an Aaron Dobson-level receiver for the Titans. Harry Douglas will soon be 32 and shouldn't be a deterrent for a young player looking to rise to the top of the depth chart.
The only player in Tennessee that could stand in Matthews' way to be #1 is sophomore receiver Dorial Green-Beckham, who led Titans receivers in yards as a rookie. That said, Green-Beckham (and Wright) are not as entrenched as a #1 receiver as Edelman is with the Patriots, so Matthews will be better able to compete for a #1 role.
The Patriots will now turn their focus towards other, older veteran free agent wide receivers like Anquan Boldin, James Jones, or even Mike Wallace.