The 21-year-old winger could make his Black Cats debut in Saturday's Premier League opener with Manchester City at the Etihad Stadium.
Januzaj, who started his career at Anderlecht, registered over 50 appearances for United before he was farmed out to German giants Borussia Dortmund last term.
The Red Devils also recently sold Paddy McNair and Donald Love to Sunderland, who are now led by their former manager David Moyes.