The 26-year-old left-back moved to the Bundesliga side on loan in January and impressed with his enthusiasm.
"We are very happy to have found an agreement," Stuttgart's director of sport Jochen Schneider said.
"Molinaro has been one of the best left-backs in the Bundesliga. He has integrated well in the group and has already become a leader."
The former Salernitana youngster also expressed his happiness at securing the move on the club's website.
"I am very happy with my decision and naturally that of Stuttgart. I wish to thank the coaches, my team-mates and all the fans.
"They have done everything since the start to help me integrate in a completely new country and atmosphere."