Voters were choosing a successor to President Ellen Johnson Sirleaf, who is stepping down after 12 years as Africa's first elected female head of state.
Results of yesterday's vote are expected in a few days, in what would be the West African country's first democratic transition since 1944, according to electoral officials.
The ballot was delayed for seven weeks due to legal challenges lodged by Boakai's Unity Party against the electoral commission over the conduct of the first round of voting, but many of the complaints appeared to have been addressed in the second round.
Former Nigerian president Goodluck Jonathan, who served as an electoral observer for the US-based National Democratic Institute (NDI), said a successful resolution to the process was of particular importance within the international community.
"This transition is critical and if we succeed, if Liberia succeeds, West Africa succeeded and Africa succeeded," he said.
"There has been no major incident to report of a technical nature and the voting was peaceful," noted electoral commission chief Francis Korkoya.
As Liberia's most famous son, Weah attracts huge crowds and has a faithful youth following in a country where a fifth of the electorate is aged between 18 and 22. But he has been criticised for his performance in the Senate, where he has served since 2014.
Weah, 51, starred in top-flight European football teams Paris Saint-Germain and AC Milan in the 1990s before playing briefly for Chelsea and Manchester City later in his career.
His rival, Boakai, 73, is seen as a continuity candidate and has won praise for his years of public service and image as a corruption-free family man, while fending off allegations he failed to tackle poverty while in government.
"I voted for George Weah because he is the one who will bring the change we have been waiting for in this country," declared supporter John Momoh after casting his ballot yesterday.
Victoria Blamoh, 56, told AFP she voted for Boakai's "experience of leadership", explaining: "He has been in government for 12 years, so he knows the ins and outs of it."
Whoever wins the election faces an economy battered by lower commodity prices for its main exports of rubber and iron ore, and a rapidly depreciating currency.
Living standards in Liberia remain among the worst in the world.
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