Shokrollah Jebeli died in Evin prison hospital in Tehran on Sunday, his son Peyman said.
Amnesty International said his treatment in jail had in effect been torture. Iran has not commented.
Mr Jebeli's death comes at a time of heightened focus on the plight of dual nationals imprisoned in Iran.
Conservationist Morad Tahbaz, a British-US national held since 2018 on spying charges, has gone on hunger strike after Iran did not release him when two British-Iranian nationals, Nazanin Zaghari-Ratcliffe and Anoosheh Ashoori, were freed on Thursday.
Iran does not recognise dual nationality and there are no exact figures on the number of such detainees.
Peyman Jebeli tweeted on an account which had campaigned for his father's release that Shokrollah Jebeli had died.
He said his father's health had seriously deteriorated in the preceding 24 hours and that his father had been made to sign a statement saying the prison would not be held responsible if anything happened to him.
Mr Jebeli had long been in poor health, had fallen over more than 10 times and had suffered a stroke in prison, according to his family. They said he was given inadequate medical care.
Last week, Amnesty said Iranian authorities were subjecting Mr Jebeli to a form of torture "by deliberately denying him adequate specialised medical care and withholding medication for his multiple serious health conditions".
The Australian Department of Foreign Affairs and Trade (DFAT) said Iran had refused to accept Mr Jebeli's Australian citizenship and had denied him "consular access".
It said the Australian government had "repeatedly sought his release on compassionate and humanitarian grounds, given his age, underlying infirmities and his illness".
According to Australian media, Mr Jebeli moved to Australia in 1976 and had made his home in Sydney, before returning to Iran in 2007.
Amnesty said two claims relating to financial disputes had been brought against him, resulting in one jail term of four years and six months, while the second case was continuing.