Shahram Amiri's mother said the body of her son had been returned to their hometown with rope marks around his neck, showing that he had been hanged.
He was later buried. Amiri had been held at a secret location after returning from the US, where he said he had been forcibly taken by the CIA.
Some reports say he had in-depth knowledge of Iran's nuclear programme.
Mr Amiri, who was born in 1977, went missing after taking a pilgrimage to Mecca in 2009.
He surfaced in the US a year later saying he had been kidnapped and put under "intense psychological pressure to reveal sensitive information" by the CIA.
In a video recording - apparently made in the US - he said: "They took me to a house located somewhere that I didn't know. They gave me an anaesthetic injection."
In another video he claimed he had escaped from US custody. He returned to Tehran in 2010 to a hero's welcome.
May or June 2009 - Shahram Amiri disappears after going on pilgrimage to Mecca, Saudi Arabia.
June 2010: emergence of videos apparently recorded in the US where a man alleged to be Amiri says he has been kidnapped and put under pressure to co-operate with the CIA
13 July 2010: Amiri reappears in Washington DC at the Iranian interests section of Pakistan's embassy, seeking to return to Iran.
15 July 2010: Amiri resurfaces in Iran where he is welcomed by officials and family members.
May 2011: Amiri is arrested and reportedly tried for treason.
August 2015: Amiri's family announces he has been executed, apparently by hanging.
