The 20-year-old joined Manchester United from Feyenoord in 2016 and been on the fringes of the first team in recent seasons.
Chong played 12 times in all competitions for the Red Devils in the 2019/2020 season, with his most recent appearance coming in the 2-1 win over Austrian side LASK in the Europa League.
Chong signed a new contract at Old Trafford until the summer of 2022 with the option for another year back in March.
"First of all, I'm happy to be here and I'm looking forward to preseason training with the team. This move is a great opportunity for me to develop. I'm looking forward to next season," Chong said in a statement.
Werder head coach Florian Kohfeldt added: "He's a very technically gifted player who can play on both wings. He's also really fast, which will help our game. Defensively he has potential for development -- he's still only at the start of his career and we want to help him continue fulfilling his potential."
Werder Bremen narrowly avoided relegation from the Bundesliga last season, finishing 16th on the table. They however got the better of Bundesliga 2 side Heidenheim in the relegation play-offs to retain their top flight status.
