The former Borussia Dortmund winger did not play a single game for Galatasaray as he completed his move to the Turkish club after the summer transfer deadline had passed
The Germany international joined Gala from Borussia Dortmund last September but the Turkish champions were unable to register him until January after failing to beat the Super Lig transfer deadline.
Their appeal to Fifa over his eligibility was unsuccessful and Grosskreutz now returns to the Bundesliga having not made a single appearance in Turkey.
Grosskreutz had been linked with a reunion with former Dortmund coach Jurgen Klopp at Liverpool, but instead joins a Stuttgart team who sit just a point above the automatic relegation places and level with Werder Bremen - who occupy the relegation play-off spot - in 15th.
"The anticipation to achieve our common goals with VfB is enormous," Grosskreutz told Stuttgart's official website. "I am looking forward to my new job and getting to know the whole team."