The crime took place in the town of Gorgan two weeks ago on the night of celebrations marking the end of the holy month of Ramadan, the Jomhuri Islami newspaper said on Saturday.
The four men broke into the house and tied up the woman's husband, the report added.
They were hanged in the main square in Gorgan on Thursday.
The men were identified as Muhammad N, Ahmad N, Alireza N, and Mujtaba S.
The newspaper said the gang had been apprehended hours after the crime, convicted by a local court and the verdict confirmed by the Supreme Court.
Rape, murder, armed robbery, apostasy and drug trafficking are all punishable by death in Iran.
When President Muhammad Khatami came to power in 1997 as a reformer, there was hope that Iran might do away with the death penalty.
But opponents say that he has made no real challenge to the ruling clergy which still dominate political institutions, the judiciary, the police and the military.