The 34-year-old only made three appearances for the club last season and, following the Serbian's fond farewell letter to the Nerazzurri, Moratti poured praise on the midfielder for his endeavours at the Giuseppe Meazza.
"I am honoured to be able to thank such a splendid person as [Stankovic] who has done Inter proud and always responded to the fans' desires with courage and character," Moratti told the club’s official website.
"He's a consummate professional who will always be loved by Inter fans and myself in particular. He'll be remembered as a battler who fought with class and courage.
"Thank you, Dejan."
Stankovic made 315 appearances throughout his nine-year spell at San Siro and won five Serie A titles, four Coppa Italia finals and one Champions League trophy during his time at the Milan-based giants.