The two clubs did not provide any further details of the transfer but the move was reportedly worth 20 million euros ($22.48 million) after months of negotiations.
"I had a good and successful time in Wolfsburg. I would like to that Wolfsburg officials for making my move to Italy possible," Perisic said in a Wolfsburg statement.
The 26-year-old joined the Wolves in 2013, netting 18 times in 70 Bundesliga matches.
Wolfsburg have also sold attacking midfielder Kevin De Bruyne to Manchester City for a reported Bundesliga record of about 75 million euros and are seen as close to signing talented 21-year-old Germany international Julian Draxler from Schalke.
(Reporting by Karolos Grohmann; Editing by John O'Brien)
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