Reports say the former AC Milan striker is all but the victor of Tuesday's run-off, as he now leads incumbent vice-president Joseph Boakai with more than 60 per cent of the votes.
During Weah's speech at Coalition for Democratic Change party headquarters, he vowed to tackle corruption.
Liberia's election run-off has been declared free and fair.
Weah extended a hand of fellowship to his rival in the just-concluded presidential runoff election and outgoing Vice President Joseph Boakai, saying he will be counting on his advice and contributions.
The US also offered its congratulations to Weah and to "the people of Liberia on the successful conclusion" of the election, which it said, "represents a major milestone for Liberia's democracy".
He is set to succeed Sirleaf, Africa's first elected female president, in what will be Liberia's first democratic handover in decades.
The lawmaker, who also congratulated Weah, pointed out that the hard work, persistence and steadfastness displayed by the football legend should be adopted by Nigerian youths in meeting their target-goals in life.
Husband Arrested After Crying Baby Leads Police To Dead Mother
Witnesses on the scene allegedly heard an argument and something falling down the stairs, The Post reports. According to the Post , police have previously responded to a domestic incident at the home.
"Weah honored Sirleaf, calling her 'the Iron Lady of Africa" and promising to 'build upon the institutional gains" her administration has made.
And the former Monaco and PSG player in his response, used the opportunity to advise the two-time African Footballer of the Year to serve his people.
This is the second time he has run for the presidency in Liberia, the first being in 2005. He played for top local clubs before starting his global career in Cameroon, then moved on to AS Monaco and Paris Saint-Germain, where he became famous.
He will take office in January.
Newly elected Liberia president George Weah has urged former Cote d'Ivoire worldwide Didier Drogba to lead his country in politics.
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.
Former FIFA World Player of the Year George Weah has been elected Liberia's new president by a wide margin as the West African nation faces its first democratic transfer of power in more than 70 years.