The ex-Germany Under-21 international has left the German outfit as he wishes to relaunch his career in Italy after failing to hold down a regular spot in five years.
Lazio has completed the signing of Moritz Leitner from Borussia Dortmund for a fee believed to be in the region of 2 million euros ($2.2M).
The midfielder, 23, already joined up with his new teammates on Thursday and has now inked a long-term deal with the Serie A side after the final details were ironed out.
Leitner came through the ranks of the 1860 Munich youth academy and joined Dortmund in January 2011.