Dybala, who moved to Palermo in 2012 from his home club Instituto, scored 13 times in 34 Serie A appearances this season, and the club had been keen to cash in on the 21-year-old, who turned down a contract extension in January.
“A fee of €32m, payable over four years, has been agreed, with a potential extra €8m to be added on if certain performance-related targets are met,” read a club statement.
“The apple is ripe and we are ready to pick it. Those who understand football realise his potential.”