Former footballer George Weah will become the new Liberian president in the country's first democratic transfer of power since 1944.
The National Elections Commission said that with 98.1 per cent of ballots counted, Mr Weah had won 61.5 per cent of the vote.
Mr Weah succeeds the continent's first elected female head of state, Ellen Johnson Sirleaf, who took over at the helm of Africa's oldest republic in 2006.
Ms Sirleaf's predecessor Charles Taylor fled the country in 2003, hoping to avoid prosecution for funding rebel groups in neighbouring Sierra Leone, while two presidents who served prior to Taylor were assassinated.
The tumultuous events of the past seven decades in Liberia, where an estimated 250,000 people died during back-to-back civil wars between 1989-2003, means a democratic handover has not taken place since 1944.
"No matter the results, we will accept it without causing problems. We don't need trouble here anymore," said Samuel Nuahn, 46, who voted for establishment candidate Boakai in Tuesday's run-off.
Initial provisional results of the ballot were due later in the day, the National Electoral Commission said , without providing further details on timing.
Local media said Mr Weah, who topped the first round of voting in October with 38.4 per cent of ballots but failed to win the 50 per cent necessary to avoid a run-off, was ahead. However, Mr Weah’s camp was already claiming victory in the second round more than 24 hours before results were known. .
Mr Boakai came second with 28.8 per cent in the first round of voting.
"The Liberian people clearly made their choice... and all together we are very confident in the result of the electoral process," tweeted Mr Weah.
Mr Weah is the only African ever to have won FIFA's World Player of the Year and the coveted Ballon D'Or -- one of football's most prestigious awards.
UN Secretary-General Antonio Guterres hailed the "peaceful conduct" of the vote, praising "the government, political parties and the people of Liberia for the orderly poll".
The Economic Community of West African States (ECOWAS) also hailed the peaceful nature of the vote.
After a vote that passed without a single major incident of violence despite weeks of delays caused by legal challenges, Liberians said they were looking forward to a peaceful handover after 12 years under Ms Sirleaf.
"Since years of civil war this is the first time we see the transition of power from one person to another. So today is an exciting moment for me especially as well as an exciting moment for Liberia," voter Oscar Sorbah told AFP after casting his ballot on Tuesday.
The Sirleaf administration, elected in 2005, guided the nation out of the ruins of war and through the horrors of the 2014-16 Ebola crisis, but is accused of failing to combat poverty and corruption.
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Mr Weah's CDC party watched their icon miss out on the presidency in a 2005 bid and was similarly frustrated when he ran for vice-president in 2011, but has repeatedly urged its young and exuberant supporters to keep cool.
"No matter what the provocation will be, CDC will not respond with violence," Jefferson Kotchie, head of the youth wing of the CDC, told supporters assembled at the headquarters of the party.
The run-off was delayed for seven weeks due to legal challenges lodged by Mr Boakai's Unity Party against the electoral commission over the conduct of the first round, but many of the complaints appeared to have been addressed in the second round.
