Dressed in black, the vice president said he would not succumb to any temptation to impose pain, agony and uncertainty on the people of Liberia.
Buhari in a statement issued by his Special Assistant on Media and Publicity, Femi Adesina commended the Liberian people on the peaceful conduct of the presidential run-off election.
"Democracy goes beyond election day, and if Liberia succeeds, West Africa succeeds, Africa succeeds, and the world succeeds".
"Wishing President-elect Weah and Liberians a peaceful transition, he reassures them of Nigeria's determination to sustain the current cordial relationship with Liberia", Buhari said.
The Nigerian leader also commended outgoing President Ellen Johnson Sirleaf, under whose 12-year watch Liberia transformed from being a pariah state to a country doing remarkably well on many fronts, such as women and civil rights issue, peace building and consolidation, ECOWAS and the Mano River Union.
The electoral board confirmed Weah's run-off victory on Friday evening, as his rival, Vice President Joseph Boakai, conceded defeat. "All we are asking is for all Liberians to come together so we can build our country".
In a nationwide broadcast from his party's headquarters in Monrovia on Friday, Mr. Boakai who was flanked by his supporters and party leaders, said he had already called Mr. Weah to congratulate him. "Weah's presidency to (have a) pro-poor, pro-growth policy that will put the people at the centre of national development", said political analyst Vita Ishmael Tue.
Moyes baffled by Bournemouth equaliser - AFC Bournemouth 3-3 West Ham United
He knows he made a mistake, but we all make mistakes. "Fortunately enough, we have another game on Tuesday, so we'll go again then".
Macron says the former soccer star and FIFA World Player of the Year still has "a special place in the French's hearts".
The South African Football Association (SAFA) on Saturday congratulated Liberian president-elect, George Weah on his recent victory in the country's elections.
Following a December 26 poll, Weah's Coalition for Democratic Change took 61.5 percent of the vote, beating Vice President Joseph Boakai's Unity Party, which got 38.5 percent.
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.
The 51-year-old Weah, a senator who entered politics more than a decade ago, will take over in January.
Weah, a retired global footballer and standard bearer of the Coalition for Democratic Change (CDC) was declared victor on Friday after the Boxing Day run-off polls by Liberia's national electoral commission. She led the country from back-to-back civil wars and saw it through a deadly Ebola outbreak that killed almost 5,000 Liberians but was criticized for not tackling corruption better.