The former Aston Villa ace decided to leave Stuttgart after losing his place in the starting XI at the club.
“In recent weeks and months things haven’t gone well for me and Christian Gross made it very clear that he has more players in my position that he is satisfied with at the moment,” said Hitzlsperger on the official Stuttgart website.
“I did all I could to perform well at the training camp but my colleagues are in good form and really don’t deserve to be left out right now. Lazio showed a great deal of interest in me and have signalled that I will play.
“Additionally, the national team coach, Joachim Loew, said that I have to be playing if I want to be taken to the World Cup. The reasons for my move are purely sporting.
“For me, this step in moving to Italy is really appealing. The move is not an escape but instead a new beginning for me. I am fit and I hope to be able to play against Catania on Sunday. I’m really looking forward to the task there.”