Mr Rafsanjani, who led his country from 1989 to 1997, suffered a heart attack in Tehran.
A leading figure in Iran since before the over-throw of the Shah in the 1979 revolution, Mr Rafsanjani often played kingmaker.
He supported current president Hasan Rouhani, who has been in office since 2013.
Under Mr Rouhani’s presidency, Iran signed a deal with the US in 2016 that curtailed its nuclear ambitions in exchange for an easing of sanctions that brought an end to more than 30 years of frosty relations with the West.
Analysts say Mr Rafsanjani’s death could be a blow to Mr Rouhani, who faces re-election in May.
A senior Iranian official described Mr Rafsanjani as “a very competent manager and a seasoned politician”.
Mr Rafsanjani was also head of the Expediency Council, a body that advises Supreme Leader Ayatollah Ali Khamenei.