The Dutch giant confirmed on its official website on Tuesday that it had accepted a bid for the Netherlands international from the Italian capital club.
The Netherlands international has enjoyed two successful seasons with the Dutch giant since moving from Utrecht in 2011, having won the KNVB Beker and the Super Cup in 2012 and becoming the Oranje vice captain.
The 23-year-old has now traveled to Rome and will negotiate personal terms before undergoing a medical check with the capital club.
"This was a transfer we could not stop," PSV technical director Marcel Brands was quoted as saying on the club's official website. "[The fee] is one of the biggest amounts in PSV's history. But it's a sporting loss."
Strootman is the second PSV star to move to Serie A this summer, after winger Dries Mertens's became Napoli coach Rafa Benitez's first signing in a 9.5 million euro June move.