A deal to bring the 20-year-old to Anfield was agreed a month ago and has now been finalised, adding to the captures of Rickie Lambert and Adam Lallana from Southampton.
The Germany Under-21 international told the club's official website: "I am proud to be a part of the family and I am looking forward to playing here. I will give it my best.
"LFC is a great club and the fans are amongst the best in the world. I am looking forward to the first game and can't wait to step on the pitch for the first time at Anfield."
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