Benmosche was AIG's president and CEO from August 2009 until last September, and is credited for turning the beleaguered company around after it made bad bets on derivatives during the financial crisis.
During his tenure, the firm repaid the $182 billion government bailout it got to avoid bankruptcy during the crisis.
"He's a huge believer in authenticity, speaking his mind, and he encouraged everybody in the company to speak their mind with candor," Hancock said.
"I think that was a critical part of what galvanized the company to take prompt action to improve its performance and turn this company around from a very, very difficult point."
Read MoreFormer AIG CEO and President Robert Benmosche dies
Hancock said Benmosche came out of retirement to run the company because his father died at a young age without life insurance, and he "recognized the critical role insurance plays in dealing with life's uncertainties."
It was the former CEO's charismatic personality that persuaded Hancock to join him at the firm and ultimately succeed him.
"His courage shines through but he also has a wonderful empathy for people. He understood the concerns that all stakeholders of AIG would be feeling but he had a vision of what the company could be if everybody pulled together. I felt if anyone could pull everyone together, he was the one."
Benmosche's legacy has made his job easier, Hancock said, because he was always supportive and helpful.
"I feel him at my side today as a source of inspiration."
—CNBC's Katie Little contributed to this report.