"He has been handed over and we will hand him over to the Philippine authorities," the official said on Tuesday.
Manila ignored criticism from the United States and Iraq's interim government, and completed the withdrawal of its 51-member contingent of troops on Monday in response to demands from the captors.
The Philippines ambassador in Baghdad could not be reached, and a source at the embassy said he had heard nothing.
Captors threatening to behead Angelo de la Cruz had set a 20 July deadline for Philippine troops to leave Iraq.
Dozens of foreigners have been seized since April to press demands for foreign troops to leave Iraq, to deter foreigners from working with US forces or to extract ransoms.
Many captives have been freed, including an Egyptian released on Monday, but at least four have been killed.