The man's wife, who presented police with video evidence of her husband's infidelity early this year, had asked the courts to spare the pair the death penalty, the Shargh daily said.
But her father demanded that the death sentence be imposed and the court found in his favour, the paper added.
Iranian law provides that if a victim's family forgives the accused in a capital crime, the convict can be either pardoned or given a jail sentence.
Under the interpretation of Islamic sharia law in force since Iran's 1979 revolution, adultery is punishable by stoning.
But Tehran changed the law in 2013 to allow judges to order an alternative method of execution, usually hanging.
It was unclear what form of execution the court ordered in the latest case.
According to human rights group Amnesty International, Iran carried out 246 executions last year, just one in public.
It gave no breakdown of the number carried out for adultery.
