The 31-year-old has signed a three-year contract at Wolfsburg and will cost the club around £1.6million.
Managing director Dieter Hoeness said: “We are glad that Arne has decided to join us and that this issue has now been dealt with.
“He is currently proving his class with the national team. Arne will not only do our team good since he is an experienced and strong-performing player, but also with his personality.
“He will certainly help us to stabilise our defence.”
