Kluivert has joined from AS Roma for a fee of £9.6m and has signed a long-term contract at the Vitality Stadium.
The 24-year-old could not establish himself at AS Roma after joining them from Ajax Amsterdam in the summer of 2018, spending the last three seasons on loan at RB Leipzig, Nice and Valencia.
He is the son of former Netherlands international Patrick Kluivert.
Bournemouth chief executive Neill Blake said: "We are delighted to have made Justin our first signing ahead of the new season. 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.
"Although he only recently turned 24, Justin has a wealth of experience and has played domestically at the highest level in five different countries.
"He has also played in the Champions League and Europa League as well as being capped by his country at senior level.
"We are all very much looking forward to working with Justin, a player we believe will be a great addition to our squad and someone our supporters will enjoy watching."
Kluivert has won two caps for the Netherlands national team.
