The new five-year contract will keep the 18-year-old winger at United until the summer of 2018.
United boss David Moyes said: "I'm delighted that Adnan has committed his future to United. He is an outstanding talent and has impressed me consistently since I came to United in July.
"His balance, poise and ability to beat players is truly exceptional for a boy of his age.
"It's great that he recognises that this club, with its tradition for developing young players and giving them a chance on the biggest stage, is the best place for him to be."
Januzaj added: "It's a great thrill to be able to sign for Manchester United. Since arriving here I have always felt like this was the right club for me.
"This season has been great for me - going on the pre-season tour, making my debut in the Community Shield win at Wembley and then breaking into the team at Sunderland - it's like a dream. I want to work hard now and establish myself as a Manchester United player."
Januzaj joined United from Belgian giants Anderlecht in the summer of 2011.
"I would have played Adnan three or four weeks earlier but the circumstances didn't feel right to put him in the team for different reasons," Moyes continued.
"He's a really good football player who is going to be able to play in several positions. Time will tell what his best one will be.
"He could arguably be a centre-forward - he's that good with his back to goal - but is also very good coming in off the left or right. As he showed at Sunderland, he has a goal in him as well."