Kluivert, 23, joins the Spanish side on an initial loan deal until 30 June 2023.
The agreement includes an option for the transfer to be made permanent.
Kluivert joined the Giallorossi in the summer of 2018, going on to make 68 appearances in all competitions – scoring nine goals.
Over the course of the last two seasons he has spent time on loan at RB Leipzig and, last season, OGC Nice.
The club would like to wish Justin the best of luck for this new adventure.
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