"The figures show that Ahmadinejad is the winner," Interior Ministry spokesman Jahanbakhsh Khanjani was quoted as saying by Reuters.
With 24.8 million votes counted, Ahmadineijad won 61.7 percent of the votes, said an official at the Guardian Council, which must approve the elections results.
Turnout at the Friday run-off polls was about 26 million, or 56 percent, down from the 63 percent of the first round on June 17.
"It's over, we accept that we've lost," said a close aide to Rafsanjani, who was president from 1989 to 1997.
Fearing clashes between supporters of Ahmadinejad and Rafsanjani, Iran's supreme leader Ayatollah Ali Khamenei issued a decree banning victory celebrations in the morning.
"Inviting people to come out onto the streets by both sides, for any excuse, is against the greater interests of the country," official media quoted him as saying.
The election has been seen as the most critical since the 1979 Islamic revolution, and emotions have been running high.
By taking office in August, Ahmadinejad will become the first non-cleric president in the Islamic republic, Reuters said.
High Hopes
Ahmadinejad is the Tehran mayor and was a former member of the special forces of Iran's Revolutionary Guards.
His humble lifestyle and pledges to tackle corruption and redistribute the country's oil wealth made a direct appeal to Iranians suffering from unemployment, inflation and corruption.
"I vote for Ahmadinejad because he wants to cut the hands of those who are stealing the national wealth and he wants to fight poverty," said Rahmatollah Izadpanah, 41.
During the run-up to the polls, Ahmadinejad insisted that freedom in Iran "is already beyond what could be imagined", and his campaign team promised "a government of justice and transformation that will make people happy."
Rafsanjani voters, on the contrary, said they feared Ahmadinejad would reverse modest reforms made under former president Mohammad Khatami.
"We have really looked at the candidates closely and we have voted for Ahmadinejad as everything that has been said about him is propaganda," said fashion conscious 18-year-old Zahra, who voted for Ahmadinejad with her sister.
Scornful Washington
Reacting to the vote results, Washington was quick to pour scorn on Ahmadineijad's choice, reported Agence France Presse (AFP).
"We have seen nothing that dissuades us from our view that Iran is out of step with the rest of the region and the currents of freedom and liberty," State Department spokeswoman Joanne Moore said.
"We remain skeptical that the Iranian regime is interested in addressing either the legitimate desires of its own people, or the concerns of the broader international community."
Ahmadineijad's stunning win of the Iranian presidential elections was seen as an end to years of tentative rapprochement with the West, according to Reuters.
"This all but closes the door for a breakthrough in US-Iran relations," said Karim Sadjadpour, Tehran-based analyst for the International Crisis Group.
"I think Ahmadinejad is less amenable to compromise on the nuclear issue, but it is unclear how much influence he will have on it."
The United States accuses Iran of having a secret program to manufacture nuclear weapons.
Tehran staunchly denies the allegations and the head of the UN nuclear watchdog Mohammad El-Baradie reiterated that there was no evidence Iran was developing nuclear weapons.