The striker has put pen to paper on a three-year deal and will link up with Boro's Under-23s.
George Miller, 19, has joined from League One Bury after impressing as he worked through the youth set up at Gigg Lane.
Miller has been watched by scouts from several clubs, alerted to his ability in front of goal as he amassed the highest goals to minutes ratio of young players in League One.
"Boro is a great club with big ambitions and this move is a big step up for me."George Miller
Born in Bolton, he is the nephew of former Premier League referee Mark Halsey.
After watching from the subs' bench for a few games, he made his league debut in February 2016 and to date has played 29 games and scored seven goals for the Shakers.
"It’s been a manic few days," said the striker after finalising his move to Teesside. "I’ve had to completely move my life up here.
"I got a call from my agent saying there was interest but it was quite a drawn out process. Then this week it’s all come together.
"Boro is a great club with big ambitions and this move is a big step up for me. I want to play well with the Under-23s and then hopefully get into that first team because that’s where everyone wants to be.
"I knew this was a big club and I’ve been here before when I was in the academy at Bury. It’s really exciting to be here and I’m looking forward to it."