Kluivert, son of ex-Netherlands striker Patrick Kluivert, has joined for a reported 11.2 million euros.
The Dutchman spent last season on loan at LaLiga outfit Valencia, where he scored eight goals in 29 games.
"We are delighted to have made Justin our first signing ahead of the new season," Bournemouth chief executive Neill Blake said in a statement.
"He was coveted by a number of clubs across Europe and his arrival is a sign of his ambition, which is matched by ours.
"Justin is an exciting and versatile attacking player who has an eye for goal. He is pacey, direct and boasts a high level of technical ability."
Kluivert, who has two caps, also had loan spells with Bundesliga side RB Leipzig and Ligue 1 team Nice.
Bournemouth added that the forward is expected to join them for the start of pre-season early next month before the squad travel to Marbella for a pre-season training camp.
Bournemouth face Maccabi Tel Aviv in Marbella on July 16th before hosting Atalanta two weeks later and Lorient on August 5th.
