The 23-year-old Dutch international joined the Giallorossi in a deal worth round £15m, although a number of clubs - including Manchester United - were rumoured to be interested.
"I didn't really know the coach, but he is one of the reasons why I am here," he told La Gazzetta dello Sport. "I spoke to him on a couple of occasions before I joined and I liked him. He filled me with enthusiasm by telling me how he wanted me to play.
"No side seriously came forward for me apart from Roma. I also asked [former AC Milan midfielder] Mark van Bommel and [ex-Roma goalkeeper] Maarten Stekelenburg for information.
"I'm happy to be here and I like the project at this club. I know that the last two seasons have not gone well, but I can't wait to get started. I hope to become a leader at this club."
Strootman moved to PSV - along with now-Napoli winger Dries Mertens - from Utrecht in 2011.