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.
Cherries manager Eddie Howe admitted his delight at the capture, claiming the Championship winner had brought in a player with “huge potential”.
“We are loaning a player of huge potential, again we had to fight off several other Premier League clubs to get him, so we are very, very pleased.
“I think he will bring pace and ability to beat a man one-v-one which is very important in the Premier League, so for all those reasons I think he is a great signing for us.”
Atsu becomes Howe’s fourth signing since promotion to the Premier League following the arrivals of Artur Boruc, Adam Federici and Josh King.