Ruhollah Zam's website and a channel he created on the popular messaging app Telegram had spread the timings of the protests and embarrassing information about officials that directly challenged Iran's Shiite theocracy. A series of televised confessions have aired in recent months over his work.
Iran's Islamic Revolution Guard Corps (IRGC) said previous year that it had used "modern intelligence methods and innovative tactics", which enabled it to "deceive" foreign services and arrest Zam.
Zam ran a channel on the messaging app Telegram that spread messages about upcoming protests in 2017 and shared videos from the demonstration.
Esmaili said Zam has also been sentenced to prison terms for lesser charges.
The sentence can be appealed before the supreme court, he said, quoted by the judiciary's official website.
The cleric wrote a letter published by Iranian media in July 2017 in which he said he would not support his son over AmadNews' reporting and messages on its Telegram channel.
At the time, he was accused by authorities of playing an active role in anti-government protests sparked by economic hardships during the winter of 2017-2018. Zam, who has said he fled Iran after being falsely accused of working with foreign intelligence services, denied inciting violence on Telegram at the time.
The IRGC alleged that Zam was "under the guidance" and protection of intelligence services in France, Israel and the US.
Esmaili claimed that most of those arrested in the protests have been released from custody but added: "There are a few who rioted, set fire to public property, and worse than that, killed people".
During his trial by the Revolutionary Court the 46-year-old Zam refuted all the charges brought against him by the prosecutor, including the charges of "collusion to take criminal action against national security", espionage, and "insults against sanctities".
Zam, the son of reformist cleric Mohammad Ali Zam, can appeal the verdict.
Iranian officials disclosed last July that Adelkhah had been arrested on espionage charges.
The claims against Zam or the protesters can not be verified as security related trials in Iran are held behind closed doors without due process of law.
Adelkhah and her French fellow researcher, Roland Marchal, were held in Iran's Evin Prison. He had been granted political asylum in France, having been imprisoned in Iran after the disputed 2009 presidential election.