"We are allowing international matches to be staged in the cities of Erbil, Basra and Karbala," FIFA President Gianni Infantino told reporters on Friday.
He was attending a meeting of the FIFA Council in Bogota.
"FIFA has given the green light for the resumption but the organizers of the championship must take the final decision," added Infantino.
He did not give a reason for Baghdad, the country’s largest and capital city, not being permitted to host matches, but promised that the city’s application would be studied.
"Congratulations to Iraqi football fans on the return of competitive international matches to Iraqi stadiums. The hard work of improving security and stability is paying off. We hope to see sports contributing in a big way to Iraqi society," tweeted Iraqi Prime Minister Haider al-Abadi.
"In light of lifting the ban on international matches on the three beloved cities of Erbil, Karbala and Basra, I warmly congratulate sports fans across and outside Iraq," Abdulkhaliq Masoud, head of the Iraqi Football Association, told Rudaw.
FIFA's decision comes as the association pushes for the restoration of international matches in Iraq.
"As the Iraqi Football Association we made mounting efforts in order to receive the approval of the Asian Football Federation to put an end to the sanction so that our players could play at home and in front of our beloved fans."
The FIFA decision "is final" and does not require a second approval by the Asian Football Federation as they had initially raised the call to FIFA to approve lifting ban on the Iraqi stadiums.
On Wednesday, Iraq will host Qatar and Syria for a friendly tournament starting on March 21.
Saudi King Salman pledged to construct a football stadium for Iraq in early-March, following a friendly match between the two countries on February 28.
After Saddam Hussein’s 1990 invasion of Kuwait, Iraq was banned from hosting FIFA matches.
FIFA lifted the ban in 2012, but reinstated it after a power outage during a match between Iraq and Jordan in Erbil.
Iraq’s electricity grid remains strained with many homes not receiving more than 10 hours of government-provided electricity at most.
