Iraqi Kurdish prime minister Nechirvan Barzani told a press conference shortly after the announcement that he "thanked Baghdad and Prime Minister Abadi because it is he who chose to reopen the airports".
A senior officer from a force tasked with protecting Iraqi Prime Minister Haider al-Abadi was shot dead on Tuesday in Iraq's central province of Salahudin, a provincial security source said.
The decision to lift the flight ban was made "after local Kurdish authorities accepted that central authorities retake control of the two airports", the statement said.
The airports are due to open "within a few days" government spokesman Saad al-Hadithi told The Associated Press.
Relations between Baghdad and the Kurdish Regional Government (KRG) have remained tense since last September, when the KRG held an illegitimate referendum on regional independence.
Former President of the Kurdistan Region Masoud Barzani said that re-opening Kurdistan airports a good step, but issues between Erbil and Baghdad can not be "summarized" merely through airport and budget matters.
Federal customs authorities will supervise the "introduction, production and handling of materials and equipment through the two airports", the decree said.
It is not clear if the autonomous region will maintain its independent visa system after the blockade ends.
The announcement comes six months after the airports were shut to worldwide flights following a controversial referendum vote in northern Iraq's self-ruled Kurdish region that was deemed illegal by Baghdad.
Iraq's neighbouring countries, especially Turkey, Iran and Syria, fear that the Iraqi Kurds' pursuit of independence threatens their own territorial integrity by inspiring the Kurdish population in those countries to seek independence.