The 23-year-old has travelled to the Italian capital for talks with Roma coach Rudi Garcia, with a medical also due to take place later this evening.
Strootman received a hero's welcome from the Giallorossi fans on arrival at Rome's Fiumicino Airport today and is expected to put pen to paper on a move to the Serie A club in the next 24 hours.
PSV technical director Marcel Brands has insisted that he was powerless to stop the Netherlands international from leaving this summer.
He told the club's official website: "This was a transfer we could not stop. The fee is one of the biggest amounts in PSV's history, but it's a sporting loss."
Stroorman is the second PSV player to swap Eindhoven for Serie A this summer following Napoli's capture of Belgian playmaker Dries Mertens last month.