The Switzerland international's move to Villa Park comes after he emerged as one of the breakout stars of this summer's World Cup, scoring three goals as Switzerland reached the quarter-finals before losing to Argentina.
Manzambi had appeared on the verge of joining Newcastle last week after the Magpies agreed a deal with Freiburg, but Villa moved quickly to hijack the transfer, with the 20-year-old making clear Villa Park was his preferred destination all along.
"I have a big message: I'm very excited to be here and we know that together we can do big things. I'm very excited to play in Villa Park," Manzambi said.
The midfielder arrives on the back of a breakout season for SC Freiburg in the Bundesliga and in Europe, including a Europa League final appearance against Villa themselves, whom he had already faced on the continental stage before completing the move.
"I am very, very happy and I am excited to play with this club. It's a very big club in England, and they're playing in the Champions League. I've already played against Aston Villa, and for me, it was the perfect plan," he said, adding that he was looking forward to working under head coach Unai Emery.
"I could see on the pitch that he was a very good trainer. I'm very excited to be here and to be training with Unai Emery and the team."
Aston Villa's business away from Manzambi's headline arrival has also been active elsewhere in the squad. The club are close to completing a separate £38m signing of Wolves midfielder Joao Gomes, who left the Championship club's pre-season training camp in Portugal on Thursday to undergo a medical.
Manzambi's arrival gives Emery a player capable of performing multiple roles in midfield, having shown attacking flair for Switzerland at the World Cup while also operating in a deeper-lying position for Freiburg that showcased his defensive attributes.
"I'm very excited to be here and to be training with Unai Emery and the team. I'm very excited to be here with my new team-mates. It's a great place here. I feel we can do big things, and we will see. With this staff and this team, I think we can do big things," Manzambi said.
Further down the pyramid, 19-year-old academy graduate Sam Proctor has joined Shrewsbury Town on a season-long loan, becoming Salop's eighth signing of the summer. Proctor, who has won the FA Youth Cup and Under-18 Premier League title with Villa, will provide competition for Shrewsbury's regular goalkeeper Will Brook after arriving as the second loan addition since the club was placed under a transfer fee ban by the EFL until the end of the window in September, following the earlier arrival of Luton striker Joe Gbode.