Former World Bank economist Ashraf Ghani won 56.4 per cent of the run-off vote to ex-foreign minister Abdullah Abdullah's 43.5 per cent, according to preliminary results.
It's a major comeback for Ghani after the first-round election in April when eight men stood to succeed President Hamid Karzai.
Dr Abdullah's camp said the results should be discounted because of fraudulent votes.
"We don't accept the results which were announced today and we consider this as a coup against people's votes," said spokesman for Dr Abdullah's campaign Mujib Rahman Rahimi.
His rejection could trigger a standoff between ethnic groups or even secession of parts of the fragile country.
Officials said the turnout was more than eight million in the June 14 vote out of an estimated electorate of 13.5 million voters - far higher than expected, and a figure likely to fuel weeks of arguments about fraud from both sides.
The next president will lead Afghanistan at a pivotal time as US-led troops end their 13-year war against Taliban insurgents and the fragile economy struggles with declining international aid.
We cannot deny fraud: Electoral Commission
"We cannot deny fraud and violations in the process," Independent Election Commission (IEC) head Ahmad Yusuf Nuristani told reporters.
"In some cases some security forces were involved, in other cases senior government officials like the governors or lower-level officials were involved."
Nuristani emphasised that the results would now be subject to auditing and adjudication of complaints, before the official result released on about July 24.
"The preliminary result in no way means the announcement of the winner of the election," he said.
"After addressing all the complaints, the objections and the inspections, a change in the result is possible."
Last-minute talks delayed the results by nearly five hours on Monday, as both sides tried to thrash out a deal over the fraud allegations that could yet derail Afghanistan's first democratic transfer of power.
Preliminary count disputed
Abdullah has vowed to reject the preliminary result, alleging he was the victim of "industrial-scale" ballot-box stuffing, while Ghani says he has won fairly.
Central to the talks is how many of the total 23,000 polling stations will now be put through an anti-fraud audit.
"We agreed for an audit of 7000 polling stations but they had other conditions that we couldn't agree with, so for now there is only partial agreement," Ghani's spokesman Daud Sultanzoy said before the preliminary result.
Abdullah's spokesman Fazel Sancharaki said: "Our main demand was for the inspection of 11,000 polling stations under the close supervision of the United Nations. Seven thousand polling stations is not enough.
"The negotiations are still ongoing. If they produce a result, we will enter the process, otherwise ... we will not recognise it."
Both sides said the UN was involved in the talks but its spokesman declined to give further details.
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