“The death sentence for Habib Chaab … nicknamed Habib Asyud, the head of Harakat Al Nidal terrorist group was executed today, Saturday morning,” the judiciary's Mizan Online website reported.
Mr Chaab had been held in Iran since October 2020 after he went missing during a visit to Turkey.
Iran said he was arrested by its security forces.
He was put on trial in Tehran and sentenced to death on December 6 after being convicted of “corruption on earth” for heading an Arab separatist group accused of attacks in Iran.
The Swedish government said the execution was “inhumane”.
According to Mizan Online, Mr Chaab led Harakat Al Nidal, or the Arab Struggle Movement for the Liberation of Ahvaz, which Iran blames for orchestrating attacks in the south-western province of Khuzestan, including one on a military parade in the main city of Ahvaz in 2018 that killed 25 people.
The oil-rich province is home to a large Arab minority, and its people have long complained of marginalisation.
Iranian authorities accused Mr Chaab of staging attacks since 2005 “under the protection of two spy services, including the Mossad and Sapo” — Israeli and Swedish agencies, respectively.
According to the prosecution, other leaders of Harakat Al Nidal are based in Denmark, the Netherlands and Sweden, with the group receiving financial and logistical support from Saudi Arabia.
Iran executes more people yearly than any other nation except China, according to human rights groups including Amnesty International.
Mr Chaab is the third dual national to have been sentenced to death or executed in Iran this year on security-related charges, according to the judiciary.
In January, Tehran executed Alireza Akbari, a former Iranian official with British citizenship who had been convicted of espionage.
In April, Iran's Supreme Court upheld the death sentence for German-Iranian Jamshid Sharmahd, 67, over his connection with a deadly mosque bombing in 2008.
At least 16 western passport holders, most of them dual nationals, are detained in Iran.
Tehran said that all had gone through a proper judicial process.
With reporting from agencies