The Ghana international, who spent last season with Everton, becomes the Cherries' fourth signing since securing promotion to the Premier League.
Bournemouth has completed the season-long loan signing of Chelsea winger Christian Atsu.
The Ghana international spent last season on loan at Everton but struggled to make his mark under Roberto Martinez.
Despite his poor club form, the 23-year-old was able to improve his displays at international level and was named Player of the Tournament at the 2015 Africa Cup of Nations.
He has yet to make his debut for Chelsea, though he has spent further time out on loan at Vitesse.