"They were convicted of carrying out terrorist acts, including bombings of government centres and public properties in several Iranian cities," the prosecutor's office said without giving the location of the bombings.
Alamhouli, Kamangar, Heidarian and Vakili belonged to the Kurdish minority of Iran, according to the European Union and several websites that report on human rights issues.
Iranian Kurds have been fighting for their own state or self-rule enclave within the Iranian state. They claim Iran's government has been suppressing them and denying them their basic human rights.
Iran has constantly denied the accusations.
The New York-based Human Rights Watch, has previously said that Kamangar, a teacher, had been sentenced to death for having links with the PKK, which has been waging a violent campaign against Turkey.
Kamangar, Heidarian and Vakili were given the death penalty in 2006; their sentences were condemned by the European Union.
Some opposition websites have reported that Alamhouli, 28, was arrested in May 2008 in Tehran and charged with having ties with PJAK, an offshoot of PKK.
The websites said the fifth convict Eslamian was arrested in May 2008 for having links with the monarchist group Kingdom Assembly of Iran.
His younger brother reportedly was hanged two years ago for his role in the bombing of a mosque in the southern city of Shiraz in April 2008 which left more than a dozen dead and 200 wounded.
Kingdom Assembly of Iran is an Iranian opposition group to the theocratic government.
It aims to restore the constitutional monarchy that was abolished by the 1979 revolution.