An outcome is not expected until later this week, but the largely peaceful voting was itself an accomplishment given Liberia’s troubled history, which included the assassinations of two presidents, William R. Tolbert Jr. in 1980 and Samuel K. Doe in 1990, and the brutal tenure of Charles Taylor, now serving a 50-year sentence for war crimes in neighboring Sierra Leone.
The runoff was delayed by six weeks to examine a complaint by the candidate who placed third in the first round of voting. But international observers say that round was largely free and fair, and the court ultimately rejected that complaint.
Mrs. Johnson-Sirleaf did not endorse either man running to succeed her, though in a speech in September at the United Nations she spoke of the need for “the next generation of Liberians to lead the country into the future,” a comment some Liberians took to be favorable toward Mr. Weah.
Mr. Weah, a senator, placed first in the first round, with 38.4 percent of the votes. He ran for president in 2005 and 2011 against Mrs. Sirleaf Johnson; the 2011 election teetered on the brink of chaos, with the opposition boycotting the second round and a violent crackdown that killed one person and injured others.
While this year’s elections have largely been free of violence, there have been plenty of accusations and conspiracy theories. Mr. Boakai and his supporters within the governing Unity Party have asserted that Mrs. Johnson Sirleaf had condoned efforts to favor Mr. Weah, accusations she has denied.
Mabel Wilson, 32, a housekeeper at a hotel in Monrovia, said that she favored “the younger leader,” who could “move the country forward.”
But she said was discouraged by signs of low turnout at a polling station in the Sinkor neighborhood of Monrovia, the capital — low turnout is seen as favoring Mr. Boakai.
“We are feeling discouraged because the polling stations are empty,” she said. “Maybe more people are tired because it’s after Christmas but I’m going to encourage them to vote to exercise their right.”
Deborah Kiadii, 21, a first-time voter, said she cast her ballot for Mr. Boakai, as she did in the first round. “He is the best leader for our country because he knows the politicians of this country and he is an educated man,” she said, citing his record in Mrs. Johnson Sirleaf’s government. “I just want good development in this country.”
In downtown Monrovia and in West Point, the city’s largest slum, steady streams of voters floated in and out of polling booths.
Observers from the National Democratic Institute, which is based in the United States, said polling stations were better organized than in the first round of voting.
Liberia’s National Elections Commission said there were isolated incidents of voting irregularities, but no sign of widespread graft. “So far the election process has been smooth and there are marked improvements on the Oct. 10 poll,” the commission said.
Saah James, a 22-year-old West Point resident, said that Mrs. Johnson Sirleaf’s tenure had been a disappointment. The son of parents who sell iron locks and steel nails on a roadside, he is jobless and cannot afford to pursue higher education.
Mr. James said he believed Mr. Weah would fight for the underprivileged because he understands their struggle.
“Some of the struggle that I have passed through — George Weah has passed through that struggle,” he said. “George Weah is the son and the soul of this soil.”
But another young Liberian, Matthew Swen, 27, who sells electric fans and irons and extension cords, voted for Mr. Boakai, whom he saw as the more experienced candidate, arguing that he would be better for entrepreneurs and for importers.
“I have seen the construction of the roads,” he said. “I have seen light and electricity and I also see it in the rural areas. Roads never used to go there.”
Mr. Weah and Mr. Boakai held large rallies as their campaigning wrapped up on Sunday, Christmas Eve.
Mr. Weah, who was born in Clara Town, a Monrovia slum, reminded a stadium crowd of his rags-to-riches story. “I had an opportunity to change my life, and this is the opportunity I want to give you to change your life,” he said, leading the crowd in chants of “Amandla! Awethu!” — a call-and-response chant from South Africa’s struggle to topple apartheid.
Mr. Boakai, who won 28.8 percent of the vote in the first round, has dismissed Mr. Weah as a lightweight without legislative accomplishments. His supporters have criticized Mr. Weah for choosing as a running mate Jewel Taylor, the ex-wife of Charles Taylor, the convicted war criminal.
Several voters urged fellow citizens to support the winner, no matter the outcome. “We ask God to help give us our rightful leader,” Ms. Wilson said. “Anyone who wins is our president.”
About 2.2 million Liberians are registered to vote. But Liberians often travel back to their hometowns and villages during the holidays, and may not have had enough time to return to polling stations in the urban communities where they are registered, observers said. The Supreme Court was reported to be wary of further delaying the runoff, given the need to have a government in place before Mrs. Johnson Sirleaf’s term ends on Jan. 15.