“I want to declare that we, the party that supports and puts forward Joko Widodo and Jusuf Kalla [for vice-president], has won,” PDI-P party chairwoman Megawati Sukarnoputri told a news conference.
One leading news website, kompas.com, put Jokowi’s final tally at 53.15 per cent, but gave no source for the data.
He will now take office in October for a five-year term.
However the man expected to be runner-up, former general Prabowo Subianto, said he was pulling out of the final count, suggesting he may mount a challenge in the constitutional court.
“The election process is problematic and not democratic,” Prabowo, a former special forces commander, told reporters in Jakarta.
His nephew and MP in his Gerindra Party, Aryo Djojohadikusumo, said: “We have withdrawn from the vote tabulation process.”
He said he was clarifying earlier comments that his uncle also planned to withdraw as a candidate.
The Prabowo camp alleges mass cheating in the 9 July ballot, enough, they say, to overturn Jokowi’s predicted victory. But unofficial counts suggest that this would require as many as seven million votes switching over to Prabowo, which analysts say is highly unlikely.
Many private counts have given Jokowi a lead of around five percentage points.
The KPU elections commission has been widely praised for the way it has conducted the vote in the world’s third largest democracy and home to its biggest Muslim population.
“It’s reflective of a man who has dedicated the past ten years to his candidacy,” Douglas Ramage, Jakarta-based political analyst, said of Prabowo’s reaction to the result going against him.
“This was his last shot and … he has failed to achieve his life’s quest. He’s disappointed.”
The Prabowo camp earlier demanded the commission delay its announcement for two weeks so that the alleged cheating could be investigated.
Confusion over Prabowo’s position rattled Jakarta shares, which had been rising on expectations of a win by Jokowi who is seen as more investor friendly.
At one stage the main index was down 2 per cent on worries that the increasingly shrill dispute could spill over into violence. Prices later recovered.
There have been no reports of major unrest since the election. Hundreds of thousands of police and military personnel are on alert across the vast archipelago of 240 million people.
Companies cancelled events and sent their employees home due to fears of potential unrest, and Jakarta’s normally congested roads were quiet at the start of the afternoon rush-hour.
“There are a lot of rumours of instability and unrest, but cautiously I’m confident that it is implausible,” said Tobias Basuki, a political analyst at the CSIS think-tank.
Both sides had claimed victory in the closest ever presidential election in Indonesia.
The outgoing president, Susilo Bambang Yudhoyono, urged whoever loses to quickly acknowledge the outcome to avoid violence. “Admitting defeat is noble,” the president told reporters on Monday.
Jokowi, born into poverty but now governor of Jakarta, has a clean image and a reputation for competence in local government, in contrast to the autocracy, corruption and power politics that have weighed down Indonesia for decades.
Prabowo’s reputation as a strongman won him a large following among voters yearning for a return to old-style rule.
Candidates can lodge complaints with the constitutional court, as did the losers of the previous two elections since strongman ruler Suharto was forced to step down in 1998 after more than three decades in power. The court must return a verdict within two weeks and it cannot be appealed.
“It is going to take a lot to push this to court. Prabowo’s camp has to prove there was massive, systemic fraud,” Mr Basuki said.
Officials said reported irregularities had been investigated, but the number of disputed votes was only in the thousands.