The Giallorossi have officially secured the services of the 23-year-old Dutch midfielder.
Both clubs had already reached an agreement about a transfer fee earlier this month, but PSV demanded a bank guarantee from Roma before giving the green light to complete the deal.
The Serie A side has now met the Eindhoven side's demands and the midfielder, 23, who was also linked with Manchester United, says he is delighted to have joined the club.
“I can report that I have finally officially signed with AS Roma, I signed a five-year contract and I'm very excited to be able to play football at this great club,” he stated on his official site.
“It is the next step in my career development that I have gone through at Sparta, Utrecht and PSV, the club I've played with over the last two years, it has been a lot of fun."