Nearly all the results from Tuesday’s poll have been counted, the election commission says.
Mr Weah, the first African to win the Ballon D’Or football award, is leading with 39%, while Mr Boakai is in second place with 29%.
A second round between the pair is expected next month.
They lead the field of 20 candidates who competed to succeed Ellen Johnson Sirleaf, Africa’s first female elected president and a winner of the Nobel Peace Prize.
Fewer than 5% of polling stations have yet to declare results, and lawyer Charles Brumskine is in third place with 9.8%
Both Mr Weah and Mr Boakai had predicted they would win the first round of voting.
Mr Weah’s former manager on the football field, Arsene Wenger, was earlier this week apparently duped by false reports that he had already been elected president.
He told reporters: “It’s not often you have a former player who becomes president of a country. So well done, Georgie.”
George Weah, 51:
Former Fifa World Footballer of the Year
Arsene Wenger, now at Arsenal, was his coach at Monaco in the 1990s
Has the political backing of jailed warlord and former president Charles Taylor
Taylor’s ex-wife, Jewel Howard Taylor, is his running mate
Joseph Boakai, 73:
Nicknamed “Sleepy Joe”
Denies it is because he is often caught napping at public events, says it is because he is a dreamer
Vice-president under Ellen Johnson Sirleaf since 2005
Has distanced himself from her record, saying “a lot more needs to be achieved”
A Freelance Journalist, Entrepreneur and Philanthropist. Editor-in-Chief of www.233times.com. A contributory writer for Ghanaian Chronicle Newspaper. An alumnus of Adisadel College where he read General Arts. He holds first degree in Bachelor of Arts from the University of Ghana; Political Science (major) and History (minor). He has also pursued MSc Corporate Social Responsibility (CSR) and Energy with Public Relations (PR) at the Robert Gordon University in the United Kingdom. He is a 2018 Mandela Washington Fellow (YALI) who studied at Clark Atlanta University on the Business and Entrepreneurship track. His mentors are Rupert Murdoch, Warren Buffet, Sam Jonah, Kwaku Sakyi Addo and Piers Morganview all posts by: Nana Kwesi Coomson
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