The Sierra Leone news website Swit Salone reported Sunday Mahama garnered 50.7 percent of the vote to 47.7 percent for Akufo-Addo. Nearly 80 percent of the West African nation's 14.1 million registered voters cast ballots.
"Ghana is the winner," Mahama, a member of Ghana's National Democratic Congress, said after claiming victory.
Akufo-Addo, the son of a former president, represented the New Patriotic Party.
The election was monitored by African Union observers led by former Nigerian President Obasanjo, who sanctioned the results despite the NPP's claims of voting irregularities.
Mahama, who had been vice president, became president of Ghana in July when President John Atta Mills passed away suddenly.