A "small fleet" of Ababil drones was deployed to the Al Rashid airfield near Baghdad, the newspaper said on its website, citing anonymous US officials.
Tehran has also installed an intelligence unit at the airfield to intercept electronic communications between ISIS fighters and commanders.
Ababil drones, less sophisticated than US unmanned aircraft, are designed in Iran and have a nearly 10-foot (three-meter) wingspan. They are used for surveillance and are unarmed.
About a dozen officers of Iran's paramilitary Quds Force, have also been sent to Iraq to advise Iraqi commanders and help mobilize Shiite militias in the south of the country, the paper said, adding that Iran's General Qassem Suleimani recently made two trips to Iraq.
Iran is also sending two flights daily to Baghdad with 70 tons each of military equipment and supplies.
"It's a substantial amount" of material, a US official told the newspaper. "It's not necessarily heavy weaponry, but it's not just light arms and ammunition."
Tehran has amassed 10 divisions of its army and its Quds Force troops along the border, ready to act if the Iraqi capital or Shiite shrines are threatened, The New York Times added.
Asked at a briefing, US State Department spokesperson Marie Harf said she "can't confirm the specifics in those reports."
But she said "anyone in the region shouldn't do anything that might exacerbate sectarian divisions, that would fuel extremism inside Iraq."
The United States has for two weeks said Iranian aid for the Iraq crisis should be done in a nonsectarian way—by pressuring the Iraqi government to adopt a national unity government and not fuel the Sunni and Shiite conflict.
We "believe Iran could play a constructive role if it's helping to send the same message to the Iraqi government that we're sending," Harf said.
A lightning offensive by Sunni insurgents led by the Islamic State of Iraq and the Levant has overrun swathes of land north and west of Baghdad this month and threatens to tear the country apart.
The United Nations says at least 1,075 people have been killed, an estimated three quarters of them civilians, and 658 wounded in Iraq between June 5 and 22. Hundreds of thousands more have been displaced.