Chemical Ali - whose real name is Hassan al-Majid - was initially sentenced to death in June last year but legal wranglings held up the case.The execution was approved two days ago, to be carried out within 30 days.
He was convicted along with two other top officials - Hussein Rashid al-Tikriti, a senior military chief, and the former defence minister, Sultan Hashem.
The presidency, which is made up of President Jalal Talabani and two vice-presidents, has not yet approved the hanging of al-Tikriti and Hashem, says the BBC's Jim Muir in Baghdad.
The two men will remain in limbo not knowing whether they are to live or die, says our correspondent. The trio, who are in the custody of American forces, were supposed to have been hanged by October.
But the executions were delayed after Hashem became a cause celebre among Sunni politicians. Iraqi Vice-President Tareq al-Hashemi has been among prominent Sunnis who insisted Hashem had simply been a career soldier carrying out orders and should be reprieved.
Iraqi Prime Minister Nouri Maliki's administration had argued with the US embassy and demanded all three be handed over to face the gallows.Former regime leaders, including Saddam Hussein himself and his half-brother Barzan al-Tikriti, have been handed over by the Americans and hanged by the Iraqi government without significant popular or political repercussions.
The regime claimed the Anfal campaign was a necessary counter-insurgency operation during Iraq's bloody eight-year war with neighbouring Iran.Majid acquired his nickname Chemical Ali during the operation after poison gas was used.