In his resignation letter to AIG director George Miles, Golub said, "Bob Benmosche has informed the Board that he believes our working relationship as Chairman and CEO to be ineffective and unsustainable."
"At this point, I view asking the Board to choose between us would be an abdication of my responsibility to lead."
Within the past couple of weeks, Benmosche, who has been the CEO since last August, had reportedly threatened to quit if Golub didn't leave.
The disagreement arose over Benmosche's push to sell AIG's largest foreign life insurance unit -- American International Assurance -- rather than take it public.
A sale to Prudential PLC of the United Kingdom recently fell through. AIG has apparently decided to take AIA public later this year, according to several news reports.
Miller, who was elected to the board in June 2009, is chairman of MidOcean Partners.