The Ghana forward, 26, has penned a contract until June 2031 at the Etihad Stadium, where he will wear the number 42 shirt.
Semenyo's transfer represents the biggest sale in Bournemouth's history and will see the Cherries receive an initial £62.5m fee, according to reports.
City negotiated a deal cheaper than the full £65m release clause in his contract, allowing them to pay the amount across 24 months.
Bournemouth could, however, also receive a further £1.5m in performance-related bonuses and 10 per cent of any profits made on a future sale, taking the deal close to the full release-clause value.
"I am so proud to have joined Manchester City," said Semenyo in a statement on the club's website.
"I have watched City over the last decade under Pep Guardiola, and they have been the dominant team in the Premier League as well as achieving amazing things in the Champions League, FA Cup and League Cup.
“They have set the highest of standards, and it’s a club with world-class players, world-class facilities and one of the greatest managers ever in Pep.
"I have so much scope for improvement, so to be at this club, at this stage of my career, is perfect for me. It’s a real privilege to be here.
"My best football is yet to come, I am sure of that. And City are in a great position - still involved in four competitions. I really feel I can help them have a strong second half of the season.
"The Etihad is my new home. I can’t wait to play in front of the fans here, and I hope to show everyone what I can do."
"Antoine is a really exciting signing for the football club,” City's Director of Football, Hugo Viana, said.
"He made it clear to us immediately that it was City he wanted to join. His enthusiasm for this football club has been clear throughout the process.
"He has huge quality. Two great feet, pace, power, a habit of influencing games and, importantly, real room for growth and development. I am excited to see the player Antoine can become in the weeks, months and years ahead."
Semenyo joined Bournemouth from Bristol City in January 2023 and has gradually risen into one of the Premier League's top forwards.
He scored a career-best 11 league goals last season and commanded division-wide interest from the likes of Chelsea, Liverpool, Manchester United and Tottenham.
In the summer, though, Semenyo signed a new contract to stay at Bournemouth to allay fears of an exit before the start of the new campaign.
Semenyo moves to City with a record of 10 goals in 21 games already this term, with his final tally being a stoppage-time winner in Bournemouth's 3-2 win over Tottenham on Wednesday.
London-born Semenyo has played 32 times for Ghana internationally, scoring three goals.