The 23-year-old Dutch midfielder moved to the Stadio Olimpico from Eredivisie side PSV Eindhoven on a five-year deal after a fee was agreed between the clubs on Tuesday.
Netherlands international Strootman underlined his excitement about the challenge that awaits him in Italy
Writing on his personal website, he said: "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."
Strootman had been strongly linked with a transfer to Manchester United but instead will move to Italy, along with former PSV team-mate Dries Mertens, who joined Napoli in the close-season.
A major influence in Strootman's decision to move to Italy was Mark van Bommel, who swapped Milan for a second stint at PSV in 2012.
Strootman told De Telegraaf: "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."
After joining from Utrecht, Strootman made 53 appearances for PSV over the course of two seasons at the Philips Stadion.
