"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.
Buhari issued a statement Friday that also commended the Liberian people "on the peaceful conduct of the historic presidential runoff election".
"Democracy goes beyond election day, and if Liberia succeeds, West Africa succeeds, Africa succeeds, and the world succeeds".
Liberia's National Election Commission has declared George Weah president-elect and Jewel Howard-Taylor vice president-elect following a December 26 runoff poll.
The former FIFA World Player of the Year is set to take over from Nobel Peace Prize laureate Ellen Johnson Sirleaf, whose 12-year rule will come to an end in January 2018.
Sirleaf, he said, deserves special commendation for the statesmanship she has shown in ensuring free and fair elections that will pave the way for a peaceful transfer of political power from one democratically elected leader to another for the first time in 73 years.
In his first public comments after his rival conceded, Weah said he was "honored to join a new generation of heads of state". Vice President Joseph Boakai has accepted defeat.
Weah adds that "we have a lot to do together to accelerate the building of tomorrow's Africa".
Addressing supporters in Monrovia, Boakai promised to provide support to Weah, but he also reminded him of Liberia's fragile economy and the challenges that lie ahead.
The 51-year-old who scored 22 goals in 60 appearances for his country played for the likes of AS Monaco, Paris Saint Germian, AC Milan, Chelsea, Manchester City, Olympique Marseille and Al Jazeera.
With more than 98 percent of votes counted late Thursday, Weah had received 61.5 percent of ballots while Boakai received 38.5 percent. Macron invited him to visit, saying Weah had "a special place in the French's hearts".
Africa's first female president, Nobel Peace Prize victor Ellen Johnson Sirleaf, is stepping aside after two terms at the head of the nation founded by freed American slaves.
Weah's supporters are confident that he will better represent their interests, which they believe seasoned politician Sirleaf failed to address after more than a decade in office.