The 27-year-old had been looking to leave Stuttgart due to a lack of regular first-team action at the club this season.
Hitzlsperger had been warned by Germany coach Joachim Low, that he needed regular first-team action in order to be included in the World Cup squad.
Stuttgart confirmed the move on their official website on Sunday, saying: “With the transfer window ending on Monday, Thomas Hitzlsperger decided to join Lazio.”
