The 23-year-old will embark on a fresh chapter of his career in the Bundesliga after agreeing terms and passing his medical with the team currently sitting in third place in the German top flight.
He has previously had loan spells away from Old Trafford with Crystal Palace and Fulham.
The Netherlands international made his senior debut for the Reds in 2016, against Arsenal, after joining the club's youth ranks from Ajax.
Ole Gunnar Solskjaer selected the Dutchman at right-back for the Premier League opener this term, against his former club Palace at Old Trafford.
Tim also came off the bench in the 2-1 defeat to Istanbul Basaksehir in the Champions League in November and made what turned out to be his final appearance for the Reds in the same competition, during the last group game, away to RB Leipzig.