"Without wholehearted shareholder support for my continued leadership, a protracted period of uncertainty could undermine the progress we have made and damage the interests of our policyholders, employees, regulators, debtholders, and shareholders".
The company's share price was up about 1.2 percent on the news at $64.22 in early trading on March 9.
AIG was brought to its knees during the financial crisis and rescued by a $182 billion bailout from the government.
American International Group disclosed that Hancock was entrusted with the responsibility of the current position in September 2014 on his selection by its board.
AIG board members were frustrated by the fourth-quarter results, which included the second surprise charge in a row, people familiar with the matter said.
"I believe this is the right decision to make for the company and all its stakeholders", said Hancock, who plans to remain chief executive until a successor is named.
Hancock's plan a year ago came as billionaire activist investor Carl Icahn called for AIG to be split.
"We fully support the actions taken today by the board of AIG", Icahn tweeted on Thursday. Earlier this year, the New York-based insurer agreed to pay $9.8 billion for reinsurance coverage from Warren Buffett's Berkshire Hathaway (BRK.A) . The company's board said it will conduct a comprehensive search for a new leader, after meeting Wednesday as part of an annual review into the firm's performance.
Hancock is AIG's fifth chief executive since Maurice "Hank" Greenberg was ousted in 2005.
"Peter's accomplishments at AIG, including his role in the company's turnaround and in driving shareholder value, are immeasurable", Chairman Douglas Steenland said in a press release.
Under Hancock's tenure, AIG completed or announced 17 deals to reduce assets collectively valued at over $13 billion. The stock declined 2.9 percent this year through Wednesday, while the S&P 500 Index rallied 5.6 percent.
Hancock had said the so-called SIFI designation targeted by Icahn was not a big concern.