Atsu, from Ghana, moved to Stamford Bridge 20 months ago since when he has had loan spells with Everton and Vitesse.
The 23-year-old can play as a winger and midfielder, and has represented his country at both the World Cup Finals and Africa Cup of Nations.
In the most recent Africa Cup of Nations, earlier this year, he was named player of the tournament.
Bournemouth boss Eddie Howe said: “We had to fight off several other Premier League clubs to get him, so we are very, very pleased.
“Christian is a player with outstanding experience when you look at the career he has had. We are loaning a player of huge potential 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.”