England-born Madjo grew up in Luxembourg, who he played for three times last year before representing England's Under-17s.
The six-foot-four striker joined Villa in January for £10 million ($13.44 million) but FIFA, whose regulations limit the international transfer of players under 18, blocked them from registering Madjo, arguing he was a Luxembourg international.
Europa League winners Villa appealed against FIFA's decision to CAS, arguing Madjo was born in England and was a UK citizen.
"The court’s decision today means that Brian will be registered as an Aston Villa player and eligible to play in official competition matches for the forthcoming season," Villa posted on X.
Madjo has scored four goals in pre-season so far, including two in Villa's opening friendly against Walsall.
Villa take on European champions Paris St Germain in the UEFA Super Cup on August 12th.