Semenyo 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 have 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 Ghanaian international Antony Semenyo from Bristol City.
“The next player will join on a four-and-a-half-year deal, with the club retaining an option for next year.”
Meanwhile, Bournemouth chief executive Neil Blake added: “Antoine is an exciting player and one we have monitored for some time.
“He had 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 part of the Black Stars squad that appeared in the Qatar 2022 World Cup.