The 18-year-old Belgian-born star marked his first Premier League start for the Red Devils with both goals in the 2-1 win at Sunderland and has quickly been persuaded to stay at Old Trafford long term.
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 arrived at United in the summer of 2011 from Belgian giants Anderlecht.
Meanwhile, Moyes confirmed his initial intention was to put Januzaj in the team before he actually did.
"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," he said. "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."
"He's got no ego to him," said Moyes. "He has no problem training with the reserves or youth team. He's a real humble boy who has been well looked after by his dad and family.
"He can handle anything that comes. I've spoken to him about what he has to do. There are going to be dips at times with young boys and we'll try and look for that but I don't see it at the moment.
"Obviously I won't play him in all the games or use him all the time but we'll certainly consider using him when we think the time is right.
"When I got the job, part of it was to introduce young players. When we're in the dressing room area I see Matt Busby's comment that if you're good enough, you're old enough.
"That has near enough been the psychology through this club. The last manager put young players in when he had them and if I've got more young ones, I'll look to play them."
One area of Januzaj's future still to be resolved is who he will play international football for, with the player eligible to play for several nations, with England also a possibility once he completes a five-year residency period.
However, his father has said his son may spurn the advances of Belgium and Albania due to the unprofessional conduct of both nations.
And Roy Hodgson's hopes of persuading Januzaj to opt for the Three Lions may have been given a boost by Abedin Januzaj, who was speaking to Kosovo-based broadcaster KTV.
"I hear an official from the Albanian FA said they talked to me eight months ago, which is a blatant lie. They did a show called 'Patriot or Traitor' for my son and FSHF said they called him up. That is not true. They are not professionals," he said, in a transcript published by the Daily Telegraph.
"I am not closing the doors to Albania, because we are Albanians. However, they are closing the doors to themselves. I only deal with professionals on the issue.
"(My son) won't be engaged with Belgium because he is focused at United. They wanted him, the coach, for the game against Croatia. But, I don't like their approach either."
On England, the senior Januzaj added: "I know Roy Hodgson said he would consider having Adnan in the English squad in the future. But, as I said for Albania and Belgium, it is not something we are not considering right now. Our full potential will be focused in doing well with Manchester United."