"AS Roma has signed a contract with Hellas Verona for the transfer of Iturbe for 22 million euros (17.3 million pounds)," the club said in a statement on Thursday.
"The agreement could rise by a further 2.5 million euros depending on the achievement of particular sporting goals."
Italian media reported that the deal also included a large payment to Iturbe's agent, pushing the overall fee up to around 30 million euros.
The player was also linked with a move to Serie A champions Juventus but the Turin side distanced themselves from the transfer as they adjust to life under new manager Massimiliano Allegri.
On Wednesday, Juventus sporting director Giuseppe Marotta announced that the 21-year-old was no longer a target for the club, following the shock departure of coach Antonio Conte a day earlier and the appointment of Allegri.
Iturbe, who was also a target for AC Milan after scoring eight goals in 33 appearances for promoted Verona last season, has signed a five-year deal with a Roma side reinforcing their squad ahead of a return to Europe's elite club competiton.
Rudi Garcia's side finished second in Serie A last season and have already sealed the signings of former England left-back Ashley Cole, Urby Emanuelson and Seydou Keita.
(Editing by John O'Brien)
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