The transfer fee is reported to be around 800 million kronor, according to The Athletic, and Semenyo has signed a contract that runs until 2031.
"I am so proud to be joining Manchester City. I have followed City for the last decade under Pep Guardiola, and they have been the dominant team in the Premier League and have achieved fantastic results in the Champions League, FA Cup and League Cup," said Semenyo.
In recent seasons, the 26-year-old has established himself as one of Premier League football's most influential offensive players, and many clubs have been rumoured to be interested in signing the winger.
Semenyo joined Bournemouth in early 2023 after a spell at Bristol City. He has also represented clubs such as Sunderland, Newport County and Bath City.
