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At a star-studded ceremony on Monday night, Paris Saint-Germain forward Kylian Mbappe was announced as the first-ever winner of the prize, with Borussia Dortmund's Christian Pulisic coming in second.
Kluivert, 19, completed the top three.
The award is voted for by all the living former winners of the Ballon d'Or.
Kluivert could yet emerge victorious in the race for the 2018 European Golden Boy, an award handed out by newspapers from around Europe.
Mbappe, 2017's winner, is ineligible - with Kluivert on the final five-man shortlist alongside the likes of Liverpool's Trent Alexander-Arnold and Ajax's Matthijs De Ligt.
During Monday night's ceremony, the men's Ballon d'Or was won by Croatia's Luka Modric - while Norway's Ada Hegerberg was announced as the first-ever victor of the women's Ballon d'Or.
Former Roma goalkeeper Alisson Becker finished 25th in the running for the men's prize.
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