United have reached an agreement with the Bundesliga club and the Italian is in Germany completing the temporary transfer.
Stuttgart are currently in 10th place in the German top-flight and and have been in the market for a new striker.
Director of sport Fredi Bobic admitted Macheda has been scouted extensively and a deal was clinched following positive discussions with Sir Alex, despite competition for his services.
Macheda, who will wear No14 at his new club, is United's leading goalscorer at Under-21 level this term and was on the bench for the FA Cup third-round draw at West Ham. After previous loan stints with Sampdoria and QPR, the striker will be determined to make his mark.
"I have followed the Bundesliga and naturally know about Stuttgart," said Macheda. "I am glad that I can now play for the club.
"For me, it is about getting to know the team and what I can bring because we have a lot of interesting games in three different competitions in front of us."