Hitzlsperger, who has also played for Aston Villa in England, had been without a club since the relegation of West Ham last season.
"I am extremely happy that the transfer is complete," the 29-year-old said. "This is the start of a great collaboration."
Hitzlsperger, who won the Bundesliga title with VfB Stuttgart in 2007 but lost his spot in the national team before the 2010 World Cup, recently trained with Tottenham Hotspur to stay fit.
He will be in the squad for Friday's Bundesliga game against Borussia Monchengladbach, coach Felix Magath said.
"He told me he is well prepared so there is nothing in the way to stop it," Magath said.
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