The Netherlands Under-21 international has spent the first part of the campaign in the Bundesliga but will have hoped for more than his 13 outings, in total, for Werder.
He was an unused substitute during the 1-1 draw with Schalke on Saturday afternoon.
Club Brugge are comfortably leading the Belgian top-flight and the transfer should enable Chong to get the game-time he is seeking. They have also announced the capture of Nabil Dirar from Fenerbahce at the same time.
At 21, Chong will be looking to push on and impress Ole Gunnar Solskjaer and the United staff.