He expressed hope that his victory and his subsequent ascending the highest office of that country will strengthen the frontiers of democracy to improve the living standards of its citizens.
Counting of votes for the presidential re-run in Liberia is on-going with unofficial rumors that former football legend George Ousman Opong Weah has taken a striking lead.
With almost all ballots from Tuesday's run-off vote counted, Weah is well ahead of opponent Joseph Boakai with more than 60 per cent of the vote, BBC reported on Thursday.
President Buhari also commended the Liberian people on the peaceful conduct of the historic presidential run-off election, stressing that "this is another plus on Africa's democratic scoreboard".More news: Rockies, Davis reach record deal
Jonathan, who had just returned from Monrovia after leading the National Democratic Institute (NDI) International Elections Observation Mission to Liberia, posted the goodwill message to Weah on his Facebook page, on Friday.
The former Ballon d'or victor was on Thursday declared victor of the Liberia presidential run-off after taking 61.5 per cent of the vote from 98.1 per cent of ballots cast to beat his opponent Vice-President Joseph Boakai, who took 38.5 per cent of the vote.
"Democracy goes beyond election day, and if Liberia succeeds, West Africa succeeds, Africa succeeds, and the world succeeds".
Former President Goodluck Jonathan has also congratulated Liberia's President-elect. "I congratulate the declared victor, Mr. George Weah".