A US-chartered flight took off from Louisiana on Monday and was scheduled to arrive in Iran by way of Qatar sometime on Tuesday, according to the report.
The deportation, an uncommon instance of cooperation between the two countries, came after months of talks, the newspaper said.
The White House and the US State Department did not immediately respond to a Reuters request for comment.
US President Donald Trump plans to deport a record number of people living in the US without legal status, arguing that it is necessary after what he describes as high illegal border crossings under his Democratic predecessor, Joe Biden.
However, his administration has struggled to increase deportation levels, even as it has created new avenues to send migrants to countries other than their own.
The identities of the Iranians and their reasons for attempting to immigrate to the US were not immediately clear, the newspaper said.
The New York Times added that some had volunteered to leave after being in detention centres for months, and some had not.
Iran's foreign ministry was co-ordinating the return of the deportees, who had been given reassurances that they would be safe and would not face any problems, according to the report.
The US in February deported 119 people from different countries, including Iran, to Panama as part of an agreement between the two countries.
