"This could be the beginning of a historic era in the (Democratic Republic of the Congo) if peace holds and finally the election results are accepted", said CBS News' Debora Patta.
The machines were the focus of much concern, with the opposition and observers saying they could open the door to manipulating results.
An al-Jazeera journalist is circumspect about whether the results will be announced then.
The South African government has tweeted a photo of Mr. Ramaphosa's meeting with President Lungu.
Mr Shadary received more than 4 million votes.
The announcement of DRC's 30 December election results will likely be delayed to March or April (while four excluded localities vote), effectively extending the administration of incumbent President Joseph Kabila through this period. But one Congolese election observer group, Symocel, on Tuesday reported "major irregularities" including the disappearance of envelopes containing results from almost 120 polling stations in Kinshasa, an opposition stronghold.
Some Congolese tired of Kabila's 18-year rule, the two turbulent years of election delays and years of conflict that killed millions of people said they simply wanted peace.
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As the lengthy results were read out on nationwide television, police were deployed at strategic spots in the capital Kinshasa where, for the second evening running, many residents went home and locked their doors early.
His preferred successor, former Interior Minister Emmanuel Shadary, is facing strong opposition from Mr Fayulu, an ex-oil tycoon, and Felix Tshisekedi, son of a veteran opposition leader.
Felix Tshisekedi, leader of the Congolese main opposition party, the Union for Democracy and Social Progress (UDPS) who was announced as the victor of the presidential elections gestures to his supporters in Kinshasa, Democratic Republic of Congo.
But on Tuesday, the head of the Independent National Electoral Commission (CENI) said the panel hoped to complete the count within 48 hours.
Congo appeared ready to achieve its first peaceful transfer of power with the surprise victory Thursday of opposition candidate Felix Tshisekedi, despite clear signs that a rival opposition leader actually won in a landslide. He has two days after the announcement of official results to file official disputes. "Ridiculous", he said. "These results have nothing to do with the truth of the polls".
But pre-election studies had predicted an easy win for Martin Fayulu, another opposition candidate. The diplomats spoke on condition of anonymity because they were not authorized to speak to the press. Barred by the constitution from seeking a third term, Kabila handpicked Shadary, a loyalist former interior minister, to run for the ruling Common Front for Congo coalition, fueling suspicions the current head of state meant to retain considerable influence over his preferred successor. He is known as the "people's soldier" for leading protests against President Kabila.
He took over from his assassinated father Laurent in 2001. He was elected in 2006, and secured another term in controversial elections in 2011.
Over the past week, the United States and other key governments have urged the electoral commission to publish accurate results or face consequences.