The midfielder, 23, penned a five-year deal after joining for a fee in the region of €20 million from PSV.
The Netherlands international cannot wait to test his ability against the best teams Italy has to offer and revealed that PSV midfielder Mark van Bommel convinced him to join the Giallorossi despite interest from around Europe.
Strootman told De Telegraaf: "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, Juventus and Napoli.
"[Van Bommel] was the man with experience of Italy at PSV. 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."
Writing on his personal website, he added: "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, Utrecht and PSV, a club where I had a lot of fun."