His rival and incumbent Vice President, Joseph Boakai, is trailing behind with 38.5 per cent.
So far, 1,176,203 votes representing 98.1 per cent of the total 1,198,984 votes cast in the runoff polls have been announced.
Chairman of the National Elections Commission (NEC), Mr Jerome Korkoya, released the provisional results at the commission’s headquarters in Monrovia on Thursday.
According to Korkoya, 100 per cent vote processing has been recorded in 11 out of the 15 counties in the country.
In all, Weah has swept 14 counties, leaving only one for Boakai.
The former FIFA World Footballer of the Year has won in Gbarpolu, Grand Bassa, Grand Cape Mount, Grand Kru, Maryland, Montserrado, Rivercess, River Gee and Sinoe counties.
The vice president won in only Lofa county, with 78,140 votes representing 84.1 per cent as against Weah’s 14,789 votes or 15.9 per cent.
A News Agency of Nigeria (NAN) correspondent in Monrovia, reports that the announcement sparked wild jubilation by youths across the streets of the capital.
Peter Kollie, 25, a commercial motorcyclist, said it was a new dawn for Liberian youths.
“Our suffering and neglect by the ruling class is over. Weah is coming to change Liberia for the youths. It’s a great day for my country,” he said.
NAN reports that the announcement of results was witnessed by Head of the ECOWAS elections observation mission and former President of Ghana, Mr John Mahama.
Weah, 51, will take over from outgoing President Ellen Johnson-Sirleaf, whose 12-year tenure ends in January.
This will be the first democratic transition of power since 1944 in a country devastated by decades of civil war.