Before polling even closed, observers were investigating claims of fraud from the rival camps.
Nickolay Mladenov, the European Union chief observer, said: "We have heard various allegations from both parties, we are looking at them in detail."
While David Pottie, head of the Carter Center, set up by former US president Jimmy Carter, said he had "heard of some irregularities in a few locations" but had not received a large number of similar reports.
Kwadwo Afari-Gyan, head of the electoral commission, declined to comment on opposition claims of intimidation and fraud, saying he had not yet seen any such reports.
However, Kwesi Jonah, a scholar-in-residence at independent think-tank the Institute of Democratic Governance, said: "On the whole, the election has been peaceful, with just some queues at some of the polling stations too long and too slow."
Return to democracy
The vote is just the third election to be held in the country since Ghana returned to democracy in 1992.
The run-off vote followed joint presidential and parliamentary elections held on December 7.
The opposition NDC won the parliamentary vote, securing 114 of Ghana's 230-seat parliament.
However, the presidential race went to a run-off after none of the contenders managed to win the more than 50 per cent of ballots cast for an outright victory.
After the first round of voting, Akufo-Addo led with just over 49 per cent, with Atta-Mills on almost 48 per cent.