The men were convicted of being “enemies of God” and of attempting to topple the Islamic regime, the semi-official ISNA (Iranian Students News Agency) said.
The executions are the first to be brought against those involved in last year’s demonstrations.
Since the disputed results of the re-election of Mahmoud Ahmadinejad in June, the country has been gripped by protests.
Millions took to the streets to demand a recount of the poll in December, on the Shia Muslim holy day of Ashura.
Eight people were killed in clashes with armed security forces.
“Following the riots and anti-revolutionary measures in recent months, particularly on the day of Ashura, a Tehran Islamic Revolutionary Court branch considered the cases of a number of accused and handed down death sentences against 11 of those,” Isna said, quoting a statement from the Tehran prosecutor’s office.
“The sentences against two of these people ... were carried out today at dawn and the accused were hanged,” the news agency said, adding the sentences had been confirmed by an appeal court.
The report named the men as Mohammad Reza Ali-Zamani and Arash Rahmanipour.
“The sentences for the other nine of the accused in recent months’ riots are at the appeal stage ... upon confirmation, measures will be undertaken to implement the sentences,” ISNA added.
The two men who were executed on Thursday have been linked with a banned monarchist group called The Kingdom Assembly of Iran.
Nasrin Sotoudeh, a lawyer for Rahmanipour, told AFP that he had been subjected to a “show trial” in July.
Sotoudeh said her client was 19 when he was arrested, and that many of the charges against him related to the time when he was a minor.
“He confessed because of threats against his family,” she said.
At least 30 protesters have been killed in clashes since the elections; the opposition puts the number of deaths at 70. Some 200 activists remain behind bars.
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