The 2,000 troops are now on the ground in Iraq's Diyala and Wasat provinces, a unnamed senior Iraqi official told the Guardian.
It comes as President Hassan Rouhani said Iran was ready to help Iraq in its battle against Sunni Islamist militants.
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"If we see that the United States takes action against terrorist groups in Iraq, then one can think about it," Rouhani said at a press conference marking a year since he was elected president.
Both Iranian and American leaders have separately pledged support for the government of Iraqi Prime Minister Nuri al-Maliki in fighting advancing fighters from the Islamic State of Iraq and Syria (ISIS).
"We have said that all countries must unite in combating terrorism. But right now regarding Iraq we have not seen the Americans taking a decision yet," Rouhani said, mentioning that problems in neighbouring Syria have been made worse by Western support for rebels there.
On Friday, US President Barack Obama said Washington was considering options over Iraq short of sending troops.
"We will not be sending US troops back into combat in Iraq, but I have asked my national security team to prepare a range of other options that could help support Iraqi security forces," he said.
The jihadists, employing brutal tactics and showing no mercy for civilians and rival rebels, have taken a swathe of mostly Sunni Arab territory in northern Iraq since launching an offensive on Monday.
Their advances and boast of animosity toward Shiism -- a branch of Islam overwhelmingly practised in Iran -- have raised alarm in Tehran, with the leadership promising to fight their "terrorism."
Rouhani said Iran is ready to help Iraq, if asked.
"No specific request has been put forward, but we are prepared to help -- within the frameworks of international regulations -- if there is a request," he said.
Rejecting notions that Iran could intervene militarily, Rouhani did not elaborate but suggested the help could be in the form of providing Iraq with military advisers.
