"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," the midfielder said in the statement.
"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 Belgium club Anderlecht in 2011 but featured little for the first team and, according to British media reports, was almost sent out on loan before he managed to impress manager David Moyes during the pre-season.
Belgium are keen to persuade Januzaj, whose parents are Kosovar-Albanians, to represent the country of his birth rather than Albania.
Moyes, who took over from fellow Scot Alex Ferguson at the start of the season, 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."
United are in ninth spot in the Premier League and play Southampton at home later on Saturday (1400 GMT).
(Writing by Sudipto Ganguly; editing by Clare Fallon)
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