The scandal, dating back to 1986, centred around accusations Quattrocchi and many others took 1.3 billion dollars of bribes from Swedish firm AB Bofors for brokering the sale of 400 field guns to India.
Controversy over the deal helped topple Gandhi's government at elections three years later.
In 2004, the Delhi high court cleared Gandhi of any wrongdoing but federal investigators later pursued the case against Quattrocchi.
Attempts to extradite Quattrocchi from Argentina failed in 2007.
Following Tuesday's announcement, the opposition BJP party accused the Congress-led government of trying to finally bury the scandal.
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But Congress spokesman Manish Tiwari said: "There needs to be a closure of the case. Since 1989 it has been going on.
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People have been trying to milk it for propaganda."