Chelsea were thought to be interested in signing the 22-year-old, but Zamparini has claimed that Palermo agreed a deal worth €43m (£37.5m) with PSG for the player on Friday.
"[We] closed the deal last night around midnight," Zamparini told Radio Radio.
"Basically it's the official transfer of Pastore to Paris Saint-Germain based on a €43m fee."
The Argentine is expected to sign a five-year deal with the Ligue One side, who continue their summer spending spree following recent Qatari investment.
Pastore rose to prominence last season when he scored 11 goals in 35 Serie A matches for Palermo.