The PKK claims to have killed more than 100 Turkish soldiers but has not given a figure for fighter casualties.
Hoyshar Zebari, Iraq's foreign minister welcomed the news, saying: "We think this is the right thing for Turkey to do."
"All the Turkish troops have withdrawn and gone back to the Turkish side of the international border."
George Bush, the US president, on Thursday urged Turkey to end the incursion as soon as possible.
The army said the withdrawal decision was made "under no external or internal influence".
It said Turkey will continue to "closely watch" the activities of the PKK in northern Iraq and "will not allow threats to Turkey from this region," the statement said.
Mike Hanna, Al Jazeera's correspondent in Iraq, said: "The Turkish military insists that the decision was taken by the military alone but reports we're receving from across the border in Turkey is that questions are being raised about the Turkish withdrawal coming so soon after what appeared to be mounting US pressure on the troops to pull out."
Ahmed Danis, a spokesman for the PKK, confirmed the Turkish troop pull-out.
He said: "We are observing military movements like empty military trucks coming from Turkey. The trucks are being loaded with troops and returning to Turkey.
"If they [Turkish troops] withdraw completely it would be a victory for Kurdistan and for the PKK."
Zap is located northwest of the city of Dohuk in northern Iraq, near the Turkish border.
It is said to have a large training base for the PKK.
Al Jazeera's Hoda Abdel Hamid, reporting from the town of Zakho, said that the area had quietened down.
"The fierce fighting we have seen has decreased significantly."
The PKK, listed as a terrorist group by Ankara and much of the international community, has waged an armed separatist campaign in Kurdish-majority southeast Turkey since 1984.