Januzaj, 22, was told he could find another club this summer by United manager Jose Mourinho.
He returned from an unsuccessful campaign on loan at Sunderland and was left out of Mourinho’s squad for the pre-season tour of the United States.
Januzaj will be presented by the club on Thursday.
The Belgian joined United from Anderlecht when he was 16 and broke into the first team in 2013 during David Moyes’ ill-fated spell in charge.
Deemed good enough to take Ryan Giggs’ number 11 shirt, Januzaj – who also had a stint on loan at Borussia Dortmund in 2015-16 – signed a five-year contract extension that was not due to expire until 2018.