Though voter turnout for Wednesday's runoff was low, Weah drew support from the younger generation, which makes up a majority of Liberia's population of 4.6 million people.
"We are young people and have suffered in this country for so long," said one supporter, Love Norrision, as honking vehicles lined up outside the Elections Commission headquarters.
The commission said 56 per cent of the country's 2.2 million registered voters cast ballots in the runoff, which was contested twice in court amid claims of irregularities, with its original November 7 date delayed.
Weah led the ticket for a coalition party, the Congress for Democratic Change, with Jewel Howard-Taylor as his vice-presidential running mate. She is the ex-wife of imprisoned former warlord and President Charles Taylor, which raised concerns among some Liberians.
Weah also ran in the country's last two elections, winning the first round of the 2005 vote that eventually went to Sirleaf.
Weah is the only African ever to have won Fifa's World Player of the Year and the coveted Ballon D'Or. He starred at top-flight European football clubs Paris Saint-Germain and AC Milan in the 1990s before playing briefly in England for Chelsea and Manchester City later in his career.
Chelsea icon Didier Drogba from neighbouring Ivory Coast sent Weah a congratulatory message.
The Washington-based National Democratic Institute, which observed Wednesday's runoff, called it peaceful and commended the Elections Commission for "notable improvements since the October 10 polls". This was Liberia's first independently run election since the end of its civil wars.
The United Nations has helped to oversee past votes.
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.
Sirleaf's predecessor, Charles Taylor, fled the country in 2003, hoping to avoid prosecution for funding rebel groups in neighbouring Sierra Leone. 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 and 2003, have prevented a democratic handover from taking place since 1944.
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".
