The Iranian consulate in the Kurdish autonomous region's capital Arbil announced the Parwezkhan and Haji Omran posts were beginning work again "from Tuesday".
A Kurdish spokesman at Parwezkhan confirmed the post had "reopened officially at 0900 (local time)" after notification was received from the Iranian side.
The opening of the two posts means that all crossings on the border between Iran and Iraqi Kurdistan are now up and running after a third post at Bashmaq started working again in October.
Iraq's Kurds voted overwhelmingly in a controversial non-binding referendum in September to establish their own country, but the vote was deemed illegal by the central government.
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Neighbouring Iran and Turkey also condemned the poll over concerns that it could stir up their own Kurdish minorities.
In the wake of the vote Baghdad moved to isolate the region by imposing an international flight ban -- recently extended through February -- and urging neighbouring nations to sever links.
Federal forces then retook swathes of disputed territory from the Kurds, wrestling back control of key oil-rich regions that were a major source of income for the region.
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