Secretary-General Ban Ki-moon said in a statement he accepted the resignation with "deep regret." Ban says he is discussing possible successors with the Arab League.
Details of Annan's resignation were not immediately released. Annan had come up with a six-point peace plan to resolve the crisis in Syria, including a cease-fire that was supposed to take effect in mid-April. But the cease-fire never took hold.
Meantime, rebels battling President Bashar Assad's forces in Syria are going to get help from the United States. President Barack Obama has signed a covert directive that allows clandestine support by the CIA and other agencies. It's not clear when Mr. Obama signed the order.
U.S. officials also said the Obama administration is giving $12 million in new humanitarian aid for Syrian civilians. That will take total U.S. humanitarian relief to $76 million since Syria's conflict began last year.
There were more deadly explosions in the Syrian city of Aleppo on Thursday. Officials said seven people, mostly women and children, were killed in shelling. Fighting over the city has lasted nearly two weeks.
On Friday, the U.N. general assembly will vote on a resolution telling Assad to resign and turn over power to a transitional authority.
The Associated Press contributed to this report.