Mr Rafsanjani had suffered a heart attack, the reports said.
He served as president from 1989 to 1997 but lost to Mahmoud Ahmadinejad when he ran again in 2005.
Although Mr Rafsanjani was part of the religious establishment, he was regarded as a “pragmatic conservative” open to improving ties to the West.
His final role was head of the Expediency Council, which tries to resolve disputes between parliament and the Guardian Council.
It was the 12-member council, a dominant force in Iran that interprets the constitution, that had disqualified Mr Rafsanjani after he entered the race for the 2013 presidential election.
After his defeat in 2005, Mr Rafsanjani became openly critical of the president.