Akufo-Addo has won more than 54 percent of the vote in the race against incumbent President John Mahama, according to local radio stations PeaceFM radio and CitiFM.
Huge crowds of jubilant Akufo-Addo supporters were celebrating at the home of the 72-year-old New Patriotic Party (NPP) leader who had already claimed victory on Thursday.
Mahama, who is seeking a second term in office, pledged to respect the results of an election being seen as a test of stability of Africa's most secure democracy.
"I want to assure the nation that we will respect the outcome of the elections, positive or negative," the charismatic 58-year-old said at his Accra residence.
He called for calm and patience over the slow pace of the count after Wednesday's presidential and parliamentary vote in the resource-rich west African nation.
"Let's allow the EC (electoral commission) to carry out its constitutional mandate. We'll make Ghana proud no matter outcome," he said on Twitter.
Ghana's election agency said it would need at least 72 hours after polls closed before it would be able to publish the final official results.
Commission head Charlotte Osei told reporters that results from 210 constituencies had been tallied and that turnout was around 49 per cent.
"This is way below our history in elections so far and it's quite disappointing," she said.
Akufo-Addo had told a cheering crowd at his home on Thursday that he was "confident" he had won, drawing the condemnation of independent observers who said it was too early to call the election.
- 'Generally credible' -
The deputy general secretary of Mahama's New Democratic Congress (NDC) party also dismissed Akufo-Addo's claim.
The winner will serve a four-year term in a formerly booming country that has seen its economy slow, currency deteriorate and inflation soar.
Tensions were palpable after the election was tainted by sporadic violence in a country once hailed by US President Barack Obama for its peaceful transitions of power.
Independent observers said that the "polling and counting processes were generally credible".
Mahama, who came to power in 2012 after beating Akufo-Addo, has urged voters to "stay the course", promising to deliver more infrastructure projects.
Akufo-Addo is making his third bid for the top job.
His NPP has blasted Ghana's poor economic growth rate -- estimated at 3.3 percent in 2016, the lowest rate for two decades -- and laid out a radical vision to transform the country's economy.
Ghana's elections have been historically close, with Mahama narrowly winning in 2012 with 50.7 percent.
Akufo-Ado unsuccessfully challenged Mahama's victory in the courts.
Manji Cheto, senior vice president at Teneo Intelligence analysts, said Ghanaians appeared to have used the polls as a protest vote.
"These elections have demonstrated yet again that Ghanaians believe the polls to be the most effective way to send a clear message to their leaders about their displeasure," she said.