The Ghana forward, 26, has penned a contract until June 2031 at the Etihad Stadium and will wear the number 42 shirt.
“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," Semenyo said.
“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."
Semenyo's transfer represents the biggest sale in Bournemouth's history and will see the Cherries receive a guaranteed £62.5m fee.
City negotiated a deal cheaper than the £65m release clause in his contract, allowing them to pay the amount across 24 months.
Bournemouth could also receive a further £1.5m in performance-related bonuses and 10 per cent of any profits made on a future sale.
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 so far this term, with his final tally being a stoppage-time winner in Bournemouth's 3-2 win over Tottenham.
England-born Semenyo has played 32 times for Ghana internationally, scoring three goals.