Ellen Johnson-Sirleaf, known as the "Iron Lady", has claimed victory as the first woman to be elected president of Liberia - or anywhere in Africa.
George Weah has criticised Ellen Johnson-Sirleaf for declaring victory
With 91% of ballots counted, she had won 59% of the vote to leave her main rival, George Weah, trailing on 41%.
She told the BBC she hoped Mr Weah would join her new government after "getting over his disappointment".
But Mr Weah, who has alleged fraud, has said she shouldn't claim victory while his complaint is being investigated.
Observers declared the vote "peaceful and transparent".
"I think the results are very clear: that the Liberian people have chosen and I am humbled by the fact that they have elected me to lead the effort of reconciliation and development," Mrs Johnson-Sirleaf told the BBC's World Today programme.
Ellen Johnson-Sirleaf: 59.1%
George Weah: 40.9%
From 90.8% of polling stations
She told Reuters news agency she hoped her win in the second and final round of the election would "raise the participation of women not just in Liberia but also in Africa".
Electoral authorities have not yet officially declared a winner in the country's first presidential election after 14 years of civil war and the United Nations peacekeeping force has put extra troops on the streets in case of unrest.
The National Elections Commission has two weeks to issue the final results after they come in from remote areas of the war-ravaged country.
A senior diplomat following the election closely said he thought there had been some irregularities but that these would not influence the final outcome.
Mr Weah accuses election commission officials of illegally casting ballots in favour of Mrs Johnson-Sirleaf.
The allegation is being investigated and some of his supporters are extremely angry, saying they have been cheated, the BBC's Mark Doyle reports from Monrovia.
Some of his supporters have held small protests, chanting "No George, no peace".
But the head of the Economic Community of West African State (Ecowas) observer mission, E M Debrah, said the preliminary conclusion was that the election had been "generally peaceful, free, fair and transparent".
Mrs Johnson-Sirleaf said she hoped Mr Weah would "see reason" and accept the result and added she was ready to offer him a place in her government.
Many of Liberia's 100,000 ex-combatants from all factions in the war backed Mr Weah in the election.
But the former AC Milan and Chelsea star urged his supporters "to remain calm for the sake of peace" until investigations into the alleged fraud were completed.
Mr Weah showed ballot papers to journalists, which he said had been pre-marked for Mrs Johnson-Sirleaf and given to election officials to cast.
"The world is saying this election was free and fair, which was not true," he said at a news conference.
Mr Weah is the best-known Liberian in the world and came top in the first round of voting, with 28% of ballots cast.
Our correspondent says as a political candidate his feel-good factor is immense but his opponents say he is young, inexperienced and surrounded by political opportunists.
They say Mrs Johnson-Sirleaf, 67, a former World Bank economist, is better qualified for the job.
The "Iron Lady" received 20% of the vote in the first round and is popular with women and the educated elite.