Italian football journalist Fabrizio Romano has claimed the star has completed a £15.8million switch to the Stadio Olimpico.
Kluivert, the son of Ajax and Dutch legend Patrick, is one of the most exciting young talents on the continent.
The winger’s father has been advising him stay put in Holland for another season.
However, it looks like the hotshot has ignored that advice and opted for a move to the Eternal City.
Kluivert senior told ESPN over the weekend: “I personally said to him maybe it’s better to stay one more year at Ajax, to make some kilometres, to be important for the team
“He’s 19 years old. He’s still young, but he makes his own decisions, and as a dad, I have to stand behind all the decisions that he makes.
“It looks like he’s going to leave Ajax. I think it’s 90 per cent sure that he’s going away.