The versatile 20-year-old moves to Villa Park in a deal worth more than £52 million – a club-record fee – and on a long-term contract.
Manzambi looked bound to join Newcastle after an agreement was reached, but Villa became his preferred destination thanks to the lure of Champions League football.
Manzambi started his career at Swiss side Servette before joining Freiburg's youth team in 2023.
He made his senior debut in August 2024 and cemented his place in the club's first team.
Manzambi made 58 appearances for Freiburg – 47 of which came last season – and was key in their run to the Europa League final, where they were beaten by Villa.
Manzambi was a breakout star in this summer's World Cup, scoring three goals and assisting two as Switzerland reached the quarter-finals.
However, he was sidelined for their final two matches in the tournament with a knee injury.