The defender made over 100 league appearances for the Boro, but has been struck by a number of injury problems over the years and has has decided not to sign a new deal with the club.
Boro boss Tony Mowbray told the club's official website: "He got injured while under contract with us and the right thing to do was to allow Matthew full rehabilitation at our football club.
"We've enjoyed having him around for the past few months and he's got himself back to the point where he's been in full training for the last four to six weeks.
"He's at the stage now where he probably needs to play a football match. If you put it into context, when he got injured he was captain at our football club and a main player, but things have changed.
"Even if Matthew had signed a contract with us, to come back as number four or five centre-half and wait for that opportunity would be difficult for him. He's a boy who needs to be playing and it's almost a natural parting of the ways."
Middlesbrough last week