Iraqi Interior Ministry official Wahhab al-Taie said the 26 captives were all Qatari nationals, adding that they had been released into the custody of the Iraqi Interior Ministry.
An airport official, who asked not to be named, said the group left Baghdad on Friday afternoon on a private Qatari jet.
The Qatari hunting party, including members of the al-Thani ruling family, was captured in Iraq in December 2015 after they entered the country to hunt falcons and bustards.
No group claimed responsibility for the abductions, though some media outlets claimed that Kata’eb Hezbollah, a popular resistance group fighting Daesh Takfiris in Iraq, had been behind the kidnapping. The group has denied the allegations.
Earlier this week, Iraqi Prime Minister Haider al-Abadi said a Qatari delegation was in the country to help with the group's release.
Qatari officials did not immediately respond to a request for comment. In April 2016, the Qatari Foreign Ministry said one of the hunters and an Asian worker on the trip had been released.
The news comes as reports said the release of the hunting party was part of a swap agreement recently reached in Syria.
The Syrian government and militant groups struck a deal in March that envisaged the transfer of 16,000 people from Shia-majority Foua and Kefraya in exchange for the evacuation of militants and their families from al-Zabadani and Madaya towns in the southwestern province of Rif Dimashq.
However, the Iraqi Interior Ministry would not provide details.
Qatar is widely believed to be among the main supporters of Takfiri militants wreaking havoc in Syria and Iraq and has, therefore, drawn harsh criticism.