The Netherlands under-21 international signed a new contract in March that will keep him with United until 2022 with the option to extend it for a further year.
"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."
He joined United's academy in 2016 from Feyenoord and made his senior debut in July 2018.
"We are pleased with the progress Tahith has made since he stepped up from the academy and are looking forward to continuing to develop his talent. He has great potential; given his age, ability and work-ethic, we can see that he has a bright future at Manchester United," United manager Ole Gunnar Solskjaer said when Chong signed his extension in March.
His first-team appearances for United were limited, making just five first team appearances in the Premier League and 16 overall. He last played for the side off the bench in United's 2-1 Europa League round-of-16 victory against LASK.
Werder finished 16th in the Bundesliga and just missed relegation after an away goal in their playoff against Heidenheim helped them stay up.
Despite struggling in the league, Werder have helped develop several impressive players including Kevin De Bruyne who made his first steps into senior football with the side while on loan there during the 2012-13 season. He scored 10 goals over 33 league appearances.
The Bundesliga returns on Sept. 18 with teams in preseason throughout August.