The country‘s electoral commission said the ex-AC Milan, Chelsea and Manchester City striker had taken 61.5% of the vote from 98.1% of ballots cast.
He beat Vice President Joseph Boakai, who took 38.5% of the vote.
Mr Boakai has now conceded to Mr Weah and offered his congratulations.
Mr Weah, who tweeted: “Change is on,” succeeds Ellen Johnson Sirleaf to become president next month, the country‘s first democratic transition since 1944.
Before the official results were announced, Mr Weah tweeted: “The Liberian people clearly made their choice… and all together we are very confident in the result of the electoral process.”
The process had been delayed by several weeks after a legal challenge by Mr Boakai.
Armed police were stationed outside the polling body‘s headquarters on Thursday, as some of Mr Weah‘s supporters started their celebrations.
Mr Weah, 51, grew up in poverty in Liberia.
Image: Mr Weah also ran for the presidency in 2005
He was raised by his grandmother in one of the worst slums of Liberia‘s capital Monrovia, but he went on to have a glittering football career in the 1990s.
He played for a number of different teams in Africa before being transferred to Monaco where he was coached by Arsene Wenger.
He also played for Paris Saint-Germain, AC Milan, Chelsea and Man City.
Image: He is the first and only African player to have won the Ballon d’Or
He is the first and only African player to have won both FIFA‘s World Player of the Year trophy and the Ballon d‘Or.
This is the second time he has run for the presidency in Liberia, the first being in 2005.
He formed the Congress for Democratic Change but was defeated.
Then in 2011 he came second as a vice presidential candidate.
Image: Supporters of George Weah celebrate the result
He has been senator for Montserrado County in Liberia after being elected in 2014.
He won 38.4% of votes in the first round on 10 October, while his opponent Mr Boakai came second with 28.8%.
This triggered the run-off as neither made it past the 50% needed for an outright win.
Throughout his campaign for election, he put his focus on education, jobs, infrastructure and health care, but came under fire for “vague” policies.
He pledged to create 50,000 jobs in his first 150 days in power.