The 21-year-old will join the Bundesliga side on a short-term deal until the end of the season, and is currently finalising the switch after previous spells at QPR and Sampdoria
The Premier League leaders have reached an agreement with the side currently 10th in the Bundesliga, with the 21-year-old currently in Germany to finalise the deal.
The Italian striker is leading the Under-21s goalscoring charts at United this season, and has made three appearances for the first team.
Macheda has had previous loan spells at QPR and Sampdoria, though in both instances the clubs parted company with their managers a short time after his arrival, and Macheda says he is happy to make the move.
"I have followed the Bundesliga and naturally know about Stuttgart," Macheda told the club's official website. "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."
Macheda will wear No.14 for Stuttgart.