The ban on worldwide flights was part of sanctions imposed on the Kurdish region after it conducted a referendum in September on Kurdish independence in defiance of Baghdad's wishes.
Al-Abadi's announcement came following a meeting with police officers and employees at the Kurdish airports. "The local authorities in Kurdistan Region reciprocated to returning the federal authority to Erbil and Sulaimaniyah airports", the statement said.
"We had urged the Iraqi MPs not to approve the budget in its current draft", Prime Minister Barzani noted.
Since the air ban was enforced, all Kurdistan-bound global flights have been rerouted to Baghdad, which has also imposed entry visas to foreigners wishing to visit the Kurdistan region.
The decree announced the creation of a new Directorate for Special Protection for the airports of the Kurdistan Region, "which will be under the command and control of the Federal Ministry of the Interior". The move followed an agreement with Kurdish officials to put their two airports under federal control.More news: Varadkar rules out post-Brexit border pre-registration
It also specified that a biometric system used in Kurdistan's airports will be linked with the federal system.
It was not immediately clear whether the region would continue to maintain its independent visa system.
The decree comes amid a dispute over the 2018 budget, which the Kurds have vehemently opposed since it was passed by parliament earlier this month.
A statement by Masoum's office said in a statement that the president returned the bill to the Council of Representatives (parliament) to re-examine the draft budget for constitutional, legal and financial violations.
The Kurds, however, are not willing to accept anything less than a 17-percent share, saying there has not been a census in Iraq since 1987.
Iraq's Parliament approved the country's controversial 2018 budget bill in the absence of Kurdish politicians, who boycotted the session. It did not specify the exact percentage to be allocated to the KRG instead stipulating it would receive funds proportional to its share of the population.