The Austria international spent the second half of last season on loan at Newcastle United, scoring twice in 15 appearances.
Lazaro, 24, joins up with the Bundesliga outfit - who are based west of the Rhine river - having previously played in Germany's top flight for Hertha Berlin before moving to Serie A.
Gladbach's sporting director, Max Eberl, told Die Fohlen's official website: "We're delighted that the loan move has gone through and that Tino has chosen to come to Borussia. He is a very versatile player and adds even more strength and depth to our squad."