The versatile 20-year-old moves to Villa Park for the remainder of the season, having made just three appearances for Jose Mourinho's side this season.
Tuanzebe, who can play in both defence and midfield, has played just one Premier League minute in 2017-18 - in a 2-0 win over Everton in January - while he also played 18 minutes on the wing in United's Champions League victory over CSKA Moscow, along with the full 90 in the EFL Cup victory over Swansea City.
“I am delighted to be here," he told Villa's official website.
“It’s an exciting time at this football club and everyone is pushing for promotion – that’s the big aim, you can feel that here.
“I am determined to help this club achieve its goal.”