Semenyo has made a good start to the 2022/23 campaign after registering three goals in four appearances in the Championship.
His form has impressed Bournemouth, who decided to spend £9 million to bring him to Dean Court.
A statement from the Premier League club said. “AFC Bournemouth have completed the signing of Ghana international Antoine Semenyo from Bristol City.
“The striker joins on a four-and-a-half-year deal, with the club having an option for a further year.”
Meanwhile, Bournemouth chief executive Neill Blake added: “Antoine is an exciting player and one that has been monitored for some time.
“He has interest from elsewhere and so we are delighted to welcome him to the club.”
Semenyo has played six times for Ghana and scored one goal. He was also a part of the Black Stars that featured in the Qatar 2022 World Cup.