The Iraqi interior ministry said "all 26" were in Baghdad and would be handed over to a Qatari envoy.
The hunters were abducted by gunmen in a desert area of Iraq near the Saudi border in December 2015.
A wide-scale search was launched but very little information was known about their whereabouts or condition.
Their release is believed to be connected to a complex deal in Syria involving the evacuation of four besieged towns. However, the interior ministry would not provide details.
The Shia Muslim political parties which dominate the Iraqi government are highly critical of Qatar's role in supporting Sunni Muslim rebels in Syria.
The hunting party is widely believed to include one or several more prominent members of the Qatari royal family, although they have not been identified.
Iraq is one of several countries frequented by Gulf Arab huntsmen and falconers as they search for prey that either does not exist in their own countries or which has been almost hunted to extinction there.
Their favoured prey is the Asian houbara bustard, akin to a small turkey, and to find it and other similar species Gulf hunters often travel to Morocco, Iraq, Pakistan and Afghanistan.