With 90 percent of votes tallied Weah received 257027 while his closest rival former Finance Minister Ellen Johnson-Sirleaf got 175520. The latest results were based on votes counted from 2781 polling stations out of 3000.
The run-off is necessary because none of the 22 candidates in the October 11 polls won at least 51 percent of the vote.
Liberia was once among Africa's richest countries with vast fields of gems and valuable groves of hardwood trees and rubber plants. It has known little but strife since a first coup in 1980.
Years of war ended in 2003 after warlord president Charles Taylor stepped down in favor of a transitional government and went into exile in Nigeria.
Millionaire Weah 39 and Johnson-Sirleaf 66 who is bidding to become Africa's first elected female president emerged as early leaders from a field of 22 candidates including former warlords and wealthy lawyers.
A runoff gives Liberian voters a choice between a national sports hero who is a political novice and a longtime politician who has an impressive international resume.
Opponents had questioned whether Weah who went from a childhood in a Monrovia slum to winning the World Player of the Year award in 1995 has the qualifications or experience to be president.
"Politicians have been up there and the masses have been down for many years. It is time for the masses to go up Weah told The Associated Press in a pre-election interview.
"With all their education and experience they have governed this nation for hundreds of years. They have never done anything for the nation."
In contrast Johnson-Sirleaf vying to become the first woman elected president in Africa stresses her long resume.
Johnson-Sirleaf was a Cabinet minister until President William Tolbert's ouster in the 1980 coup. She was runner-up to warlord Charles Taylor in the 1997 presidential election.
A Harvard University graduate who has been a top official at the United Nations and the World Bank Johnson-Sirleaf is viewed by many as a strong administrator but hampered by her ties to the old political order.