The 26-year-old, who scored 18 goals in 70 Bundesliga starts, has signed a five-year deal with the Serie A club.
"I had a good time in Wolfsburg and I would like to thank them for making my move to Italy possible," Perisic said.
He was the second high-profile departure from Wolfsburg over the weekend, after midfielder Kevin De Bruyne joined Manchester City for £55m.
Perisic, who signed for Wolfsburg from Borussia Dortmund in 2013, has been capped 38 times by his country, scoring nine goals.
Inter Milan have signed Croatia striker Ivan Perisic from German side Wolfsburg for reported £14.5m.