The 18-year-old joined United two years ago from Anderlecht, with his previous deal at Old Trafford set to expire at the end of this season.
After scoring two goals on his first Premier League start against Sunderland start earlier this month, the winger had attracted the attentions of Juventus and Barcelona.
However, any hopes they had of signing Januzaj have been ended after he agreed a new contract with the Premier League champions.
Januzaj said he was delighted to have agreed the new deal, and hopes to become a first-team regular this season.
"It’s a great thrill to be able to sign for Manchester United," he told the club's official website. "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."
Manager David Moyes, meanwhile, is thrilled to have tied Januzaj down and predicted a big future for the youngster.
"I'm delighted that Adnan has committed his future to United," he said. "He is an outstanding talent and has impressed me consistently since I came to United in July.
"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."
