The 20-year-old is leaving German side Freiburg for the Premier League club that defeated them in the Europa League final in May.
Aston Villa have not disclosed the length of the contract or the transfer fee, but British media reports indicate that Aston Villa will have to pay more than £50 million, equivalent to 650 million kronor. That would be a transfer record for a Swiss player.
Manzambi scored three goals and provided two assists in four World Cup matches before injuring his knee in training ahead of the round of 16 against Colombia.
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