Hancock, who was named chief executive in September 2014, alluded to the discord with shareholders in a statement.
Hancock, who was named chief executive in September 2014, alluded to the discord with shareholders in a statement. Activists Carl Icahn and John Paulson have called for AIG to be broken up.
"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.
"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, debt holders, and shareholders."
AIG reported a loss of $3.0 billion in the fourth quarter following a hefty charge to build reserves for future losses.
The US government saved AIG from failure at the height of the 2008 financial crisis with a controversial $182 billion bailout that was later repaid in full by the insurer under Hancock's leadership.
Hancock had opposed Icahn and Paulson's efforts to break the company up, instead unveiling a cost-cutting and restructuring plan. However, the CEO was unable to win support from activists.
Icahn endorsed Thursday's developments, saying on Twitter "we fully support the actions taken today by the board of AIG."
Shares of AIG rose 1.9 percent to $64.63 in pre-market trading.