The 21-year-old has signed a three-and-a-half-year contract extension after impressing for the club this season.
“It wasn’t really a difficult decision to commit to a new contract because until my injury I’ve been in the team and happy,” Williams told the club’s official website.
“I’d had some talks with Gareth Southgate initially but it was great that Gordon Strachan came in and quickly said that he wanted me to sign a new deal.
“That’s a big boost for me, especially as he has picked me so often too.
“Now my aim is to win promotion with Boro. That’s what all the lads want and the gaffer too. We all want to get the club into the Premier League and we believe we can do it.
“If I can help Boro win promotion and play at the World Cup that would be the perfect scenario.”