Greenberg has agreed to pay a $15-million fine and Smith a $1.5-million fine to settle the charges, without admitting any wrongdoing.
Greenberg was at AIG's helm for 38 years before stepping down amid investigations into the firm's accounting practices.
AIG was brought to the brink of collapse last September and has since received government bailouts totalling more than $180 billion. The bailouts became a major headache for President Barack Obama after it emerged in March that the company paid out about $165 million in bonuses to its executives after receiving government funds.