The deal is worth a reported £47 million for the 18-year-old winger, per Sky Sports.
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The promising Senegal international scored for his country at the 2026 World Cup, and became the youngest player to score at the final's in the tournament's history.
He made his debut for PSG at just 16 years old, and has already won two UEFA Champions League titles, two Ligue 1 titles, a French Cup and two UEFA Super Cups.
Mbaye has made 33 appearances for PSG, scoring four times and providing two assists.
He will now work under boss Unai Emery at Villa Park as they look to bounce back from a poor start to the Premier League season.