The 25-year-old, who made 114 Bundesliga appearances with Eintracht and before that Kaiserslautern, has signed a five-year contract.
PSG, however, are already thought to be well served in his position with Italian goalkeeper Salvatore Sirigu and his reserve Nicolas Douchez.
However, club president Nasser al-Khelaifi said Sirigu was aware of the club's needs.
"Salvatore is a very good goalkeeper. I don’t forget that, in 2011, he was one of the first players to join us and to believe in our project," he told PSG's website.
"He helped us to build quickly a very competitive team with whom he won three titles in Ligue 1 and several other trophies.
"But if we want to compete for a place on top of European football we must have more than one strong player for each key position. As you know, it is the case in several big European clubs. Salvatore is aware of this context."
(Writing by Brian Homewood in Berne; editing by Toby Davis)
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