Strootman has signed a five-year deal with the Giallorossi after the two clubs agreed a fee reported to be 20 million euros (£17.3million).
Strootman wrote on his personal website: "I am very excited to be able to play for this great club.
"It is the next stage in my career development after being at Sparta, FC Utrecht and PSV, a club at which I had a lot of fun."
The 23-year-old admitted he had sought the advice of PSV team-mate, and former AC Milan midfielder, Mark van Bommel before opting to move to Italy.
Strootman told De Telegraaf: "He was the man with experience of Italy.
"Mark said how great the passion of the fans was, how special the atmosphere in the stadiums was and how there was a totally different football culture.
"What counts for me is the number of big games I am going to play here.
"I will train every day with top players and get to play against the likes of Inter Milan, Juventus and Napoli."
PSV technical manager Marcel Barends told the club website that it had been "an offer that was impossible to turn down, one of the biggest fees in the history of PSV".
- Sports & Recreation