"I can't help but compare it to the signing of Alves last week," Boro boss Gareth Southgate told the club's official website.
"It's so important not only to sign new players but to keep hold of your best ones. It's fantastic news as a club and we're delighted that Stewart sees his future as being here.
"He's wanted to sort it out for a while and we're delighted to have been able to come to an agreement.
He loves being here and he's one of the first in and the last off the training field.
"He's from the town and he's passionate about the team. He loves playing his football here and is involved in so many of the good things that happen for us."