Ayatollah Khamenei hailed a "companion of struggle" despite their differences, saying this was a "difficult" loss.
President Hassan Rouhani praised Mr Rafsanjani as a great man of the Islamic revolution.
The government has announced three days of mourning, making Tuesday a public holiday for his funeral in Tehran.
Mr Rafsanjani, who served as president from 1989 to 1997, was pivotal in the 1979 revolution. But later in life he became a counterpoint to hardline conservatives.
"The different opinions and interpretations at time in this long period could never entirely break up the friendship between us," said Ayatollah Khamenei.
Mr Rafsanjani died on Sunday in a hospital in Tehran after suffering a heart attack.
His body was taken to Jamaran prayer hall, the residence of the founder of the Islamic Republic, Ayatollah Rohullah Khomeini, where relatives, politicians and religious figures gathered to pay their last respects.
Mr Rafsanjani had been a mentor to President Rouhani, whom he supported after his own attempt to run in the 2013 election as a reformist candidate was rejected by the powerful Guardian Council.
Mr Rouhani said on Twitter: "The soul of the great man of the revolution, symbol of patience and resistance, has gone to Heaven."
Analysts say Mr Rafsanjani's sudden death is a major blow to the president, who is preparing for re-election in May.
Iranian newspapers across the political spectrum are paying tribute to Mr Rafsanjani. Most front pages are splashed with pictures and captions highlighting his central role in Iranian politics. Many have used black as a background.
"Iran mourns the death of contemporary Amir Kabir," moderate Arman-e Emruz announces, comparing Rafsanjani to the man widely considered to be Iran's first reformer and moderniser.
An "irretrievable loss", moderate daily Iran laments, while reformist Aftab-e Yazd, under a picture of Mr Rafsanjani's grieving children, affirms that "Iran is mourning".
Even hard-line dailies are joining in the accolades. Javan notes his closeness to the founder of the Islamic republic, Ayatollah Ruhollah Khomeini, and Supreme Leader Ali Khamenei in its headline: "Man of tough days of fighting and friend of Imam and the Leader rushes to meet God."
Hard-line Vatan-e Emrooz describes him as "one of the pillars" and "a genuine figure" of Iran's Islamic Revolution.
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BBC Persian's Kasra Naji says Mr Rafsanjani was a great survivor of the Iranian revolution, always managing to stay afloat in the unending political struggles between the hardliners and the moderates, remaining influential.
In recent years, our correspondent says, he has been a central figure in the reform movement that has been trying to have a moderating influence on Iran and Ayatollah Khamenei.
Mr Rafsanjani's final role was head of the Expediency Council, which tries to resolve disputes between parliament and the Guardian Council.
Akbar Hashemi Rafsanjani was born in 1934 in south-eastern Iran to a family of farmers.
He studied theology in the holy city of Qom with Ayatollah Ruhollah Khomeini - who went on to lead the Islamic revolution of 1979 - and was imprisoned several times under the Shah.
In the last year of the 1980-88 war with Iraq, Ayatollah Khomeini appointed him acting commander-in-chief of the armed forces.
He was seen as the main mover behind Iran's acceptance of the UN Security Council resolution that ended the war.
Mr Rafsanjani was also a key player in the development of Iran's nuclear programme, and recently gave staunch support to the landmark 2015 nuclear deal with world powers.
He was a man known for a sharp wit but who could also be ruthless.
He advocated progressive economic policies, encouraging private businesses and improving infrastructure. His own business holdings were reported to be widespread.
Mr Rafsanjani ran for a third time for president in 2005 but lost to Mahmoud Ahmadinejad.
Mr Rafsanjani became openly critical of the victorious president and in 2009, he sided with reformers who disputed that year's elections. Nevertheless, Mr Ahmadinejad won a second term.
Mr Rafsanjani continued to champion moderate causes, such as the release of political prisoners and greater political freedoms for parties prepared to work within the constitution.
Some of the members of Mr Rafsanjani's family have also made the headlines. His daughter Faezeh Hashemi attracted the ire of hardliners when she met a leader of the Bahai religious minority - which Iran's leadership regards as a heretical sect - last year.
And his son Mehdi Hashemi Rafsanjani was jailed in 2015 after being convicted of "security offences and financial crimes".
Iran's Supreme Leader Ayatollah Ali Khamenei has led tributes to former President Akbar Hashemi Rafsanjani, who has died at the age of 82.