The centre-forward is an England U17 international and has tasted first team action with Metz this season as a 16 year-old.
Madjo also has played three games for Luxembourg's youth team.
While the length of contract with Villa is undisclosed, it's believed he leaves Metz for a €12m fee.
"I’m really happy to be at this beautiful club,” he told Villa TV.
“It’s a dream for me to play in the Premier League for such a big club. My family are very happy too, so I’m really happy to be here.”
Madjo added: “The project was the one for me, the environment is very good for me and the coaching staff will help me to improve.
“This is a great opportunity for me because it’s going to make me grow.”
