It was unclear how the transaction would be conducted as Iran's access to the global banking system is targeted by international sanctions over its nuclear ambitions.
Under the terms of the contract signed in Baghdad on Sunday, Iran will eventually feed Iraqi refineries with 25 million cubic metres of gas per day, Javad Ouji said, quoted by the news website of Iran's oil ministry, Shana.
This is Iran's largest reported gas deal to date.
It has a $7.5 billion gas pipeline project with Pakistan, to export 21 million cubic metres per day, but the plan has repeatedly run into trouble amid US opposition to the deal agreed in 2010.
Iran sits on the world's second largest natural gas reserves and currently produces some 600 million cubic metres a day, almost all of which is consumed domestically due to lack of exports means.
Ouji, speaking after the signing ceremony on Sunday, said the gas export will be transported through a 227-kilometre pipeline under construction in the western province of Ilam.
It will then go through a 270-kilometre pipeline in Iraq due for completion "within one or two months," said Ouji, who heads the National Iranian Gas Company (NIGC).
The report came after Iran's outgoing President Mahmoud Ahmadinejad paid a two-day visit to Iraq.
Shia powerhouse Iran and Iraq, which fought a deadly war the 1980s, have become close allies since the 2003 fall of Saddam Hussein and the rise to power of a Shia-dominated government in Baghdad.
According to Ouji, the two neighbours are also considering a second contract for an additional daily amount of 20 million cubic metres of gas to be exported to Iraq.
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