"Warm congratulations to George Oppong Weah on his decisive victory in Liberia's peaceful presidential run-off, thus becoming the next President of the Republic Liberia", Akufo-Addo wrote on via his official Facebook account.
With more than 98 percent of votes counted late Thursday, Weah received 61.5 percent of ballots while Vice President Joseph Boakai received 38.5 percent.
Voter turnout was 55.8 per cent, or just over 1.2 million people, the NEC reported.
The former FIFA World Player of the Year played with AS Monaco and Paris Saint-Germain, among others.
"Some people do not believe that Ambassador Weah has what it takes to perform as President, but they should wait and see; the man will surprise them, " he said.
"Although we worked so seriously for a different outcome than what [the] results show, my faith, values and principles dictate that I respect the will of the people as announced by the National Elections Commission", Boakai said.
"George Weah is very humbled by what is happening in Liberia now", he told Asempa FM.
Weah responded: "I am honoured to join a new generation of heads of state".
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"Weah honored Sirleaf, calling her 'the Iron Lady of Africa" and promising to 'build upon the institutional gains" her administration has made.
The President of Sengal, Macky Sall, also congratulated Weah on Twitter and wished him "much success". "Weah's rags-to-riches story has been an inspiration to many supporters who call him 'King George".
"Together, let's help speed up the development of our continent", Weah wrote.
Mr Weah, who tweeted: "Change is on", succeeds Ellen Johnson Sirleaf to become president next month, the country's first democratic transition since 1944.
He was raised by his grandmother in one of the worst slums of Liberia's capital Monrovia, but he went on to have a glittering football career in the 1990s.
Weah is expected to take office in January.
The 51-year-old Weah, a senator who entered politics after his 2002 retirement, led the first-round election in October but didn't receive enough votes to win outright. He played for top local clubs before starting his worldwide career in Cameroon, then moved on to AS Monaco and Paris Saint-Germain, where he became famous.