The German coach will succeed Unai Emery who will leave the club at the end of the season. The 44-year-old has coached the likes of Augsburg II, Mainz and Dortmund where he won the DFB-Pokal in the 2016-17 season.
The Ligue 1 champions had a disappointing campaign in the UEFA Champions League, losing out to Real Madrid in the prequarter-finals which ultimately led to Emery's departure.
He was chosen by PSG over a list of candidates reported to have included Juventus' Massimiliano Allegri, Chelsea's Antonio Conte, Tottenham Hotspur's Mauricio Pochettino -- a former PSG captain as a player -- and Andre Villas-Boas.
His task will be to manage a dressing room full of high-profile personalities including Neymar, Edinson and marco verrati.