Sources told ESPN the striker cost Hertha a fee in the region of €27 million.
The Poland international moved to San Siro from Genoa 12 months ago as a replacement for Chelsea-bound Gonzalo Higuain following a stellar start to life in Serie A in which he scored 14 goals in his first nine matches in Italy.
However, he has scored just six times in his last 28 matches for the Rossoneri and has moved on following the arrival of Zlatan Ibrahimovic earlier this month.
Hertha, managed by former United States manager Jurgen Klinsmann, saw German businessman Lars Windhorst buy a stake in the club for €142m in the summer -- the largest single largest equity transaction in Bundesliga history.
Piatek has become the first major signing under the new ownership and the most expensive in the club's history. Hertha sit 13th in the Bundesliga table.