Voters have chosen a successor to President Ellen Johnson Sirleaf, who is stepping down after 12 years as Africa's first elected female head of state, representing the West African country's first democratic transition since 1944.
AFP journalists saw polling stations closing at 6:00 pm (1800 GMT) as counting was due to begin, while results are expected in the next few days, according to the electoral commission.
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.
"Turnout was significantly slower during the morning than for the first round election," noted the Liberia Elections Observation Network, which had more than 1,000 observers stationed across the country, echoing a similar statement earlier by the European Union's chief observer.
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.
Vice President Boakai, 73, meanwhile 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.
The two candidates voted at polling stations near their homes in Paynesville, a suburb of Monrovia, the capital of this nation of 4.6 million people.
Both declared victory was theirs for the taking.
But Weah was resolute that his second run for the presidency would be successful after 12 years spent building a political reputation to match his popularity.
"Victory is certain," he told journalists after casting his ballot.
Weah topped the first round of voting with 38.4 percent while Boakai came second with 28.8 percent. That triggered a run-off as neither made it past the 50 percent needed to win outright.
Whoever wins on Tuesday 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.
"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 voting.
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."
Charles Taylor is serving a 50-year sentence in Britain for war crimes committed in neighbouring Sierra Leone, but his presence has loomed over the election.
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