Ghana forward Antoine Semenyo (R) has joined Bournemouth. Photo: Khaled DESOUKI / AFP/File
Semenyo agreed a four-and-a-half-year contract, with Bournemouth holding an option to extend the deal for a further year.
The 23-year-old is Bournemouth's third signing of the January transfer window after goalkeeper Darren Randolph and Burkina Faso forward Dango Ouattara.
Semenyo, who featured for Ghana at the World Cup in Qatar last year, scored 21 goals in 125 games for Bristol City.
"Antoine is an exciting player and one we have monitored for a while," Bournemouth chief executive Neill Blake said.
"He had interest from elsewhere and so we're delighted to welcome him to the club."
Bournemouth boss Gary O'Neil will hope Semenyo can make an immediate impact in their fight against relegation.
The Cherries are languishing in 18th place in the Premier League after winning promotion from the Championship last season.
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