"Even when I went on loan, I always said I wanted to come back to Middlesbrough," he added.
"There's no reason why I can't achieve things with my hometown club. I want to captain the team and I want to win something."
McMahon's injuries include a broken leg, dislocated shoulder and knee problems, and manager Southgate paid tribute to his character.
"Tony's had a long battle back from two very serious injuries and he's got himself back in the first team squad," he said.
"He warrants a new contract on what he has achieved in recent months.
"There are still big challenges ahead for him to try and force his way into the team regularly, but he has shown tremendous character to come back from the injuries and show people that he is able to play at this level.
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