The Dutch giants confirmed on their official website on Tuesday that they had accepted a bid for the Netherlands international from the Italian capital club
The Netherlands international has enjoyed two successful seasons with the Dutch giants since moving from Utrecht in 2011, having won the KNVB Beker and the Super Cup in 2012, becoming Oranje vice-skipper.
The 23-year-old has now travelled to Rome and will negotiate personal terms before undergoing a medical check with the capital club.
"This was a transfer we could not stop," technical director Marcel Brands was quoted as saying on their official website.
"[The fee] is one of the biggest amounts in PSV's history. But it's a sporting loss," he added.
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 June move.