A cargo plane carrying electronic devices touched down from the United Arab Emirates, an AFP correspondent said.
It was followed by a Royal Jordanian plane, with 39 passengers on board, which took off for Amman, said Dana Mohammed, a spokesman for Sulaimani airport.
They were the first international flights since Baghdad imposed a ban in late September on autonomous Iraqi Kurdistan's two airports -- in Sulaimani and the regional capital of Erbil.
The federal government imposed the air blockade after Iraqi Kurdistan voted overwhelmingly for independence in a non-binding referendum rejected as illegal by Baghdad.
Baghdad lifted the ban last week "after local authorities in Kurdistan agreed to the central authorities taking control of both airports", Prime Minister Haider al-Abadi said.
The flight ban was part of a battery of penalties inflicted on the Kurds as Baghdad sought to nullify the poll.
Federal forces also retook swathes of disputed territory, wrestling back control of oil-rich regions held by Kurdish forces since 2014 in battles against the Islamic State group.
During the blockade, all flights between Iraqi Kurdistan and foreign countries transited through Baghdad.
Foreigners who previously did not have to apply for a visa to visit the Kurdish area must now do so through the authorities in Baghdad.
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