The 19-year-old, the son of legendary Oranje striker Patrick Kluivert, has signed a five-year deal with the Serie A club.
Ajax have also secured a 10% sell-on fee for any future transfer that earns the Italian side more than €25m (£22m).
"I'm feeling great," Kluivert told the Roma website. "I'm at an unbelievable club and I can't wait to start.
"I think Roma is a great club for me - I think they can build me into a bigger, stronger player and I can do some nice things here."
Roma sporting director Monchi added: "I think that Justin is already one of the most exciting young players in European football.
"Because of this it was not easy to bring him to Roma ahead of a number of other clubs. But Justin believes Roma is the perfect club for him to continue his development and realise his enormous potential."
Kluivert, who was previously linked with a move to Manchester United, hit 10 goals in 30 appearances last season and won his first senior cap for the Netherlands in March.