Wiese's contract was due to expire in the summer of 2016, and with the player unhappy the club's CEO Peter Rettig said that it was important to strike a deal for his exit.
"The aim was to find a sensible solution for all involved and we're very relieved that we have managed this," Bundesliga.com quotes Rettig as saying. "We have managed to resolve the issue to our satisfaction."
Wiese said that he is glad to finally be able to consider another club and that he and his family can now be happy.
"This is a foundation which opens up more options and perspectives," he said. "After a not particularly easy time for me and my family, I can now look forward and consider my future."
Wiese played for Werder Bremen between 2005 and 2012.