It is a public holiday and people are glued to their radios and television sets as the results trickle in.
A number of ministers have lost their seats in the parliamentary elections.
Poll officials reported a huge voter turnout and monitors hailed the exercise as a shining example of democracy in action for Africa.
President John Kufuor, 70, is stepping down in January after serving the maximum two terms.
The main contest is between Mr Kufuor’s governing New Patriotic Party (NPP) and the opposition National Democratic Congress (NDC) of former ruler Jerry Rawlings, which was in power until eight years ago.
The leading contenders are ex-Foreign Minister Nana Akufo-Addo and the NDC’s John Atta Mills, who is a presidential candidate for the third time. The winner is expected to be named later on Monday.
But the electoral commission has until Wednesday afternoon to release the final official results.
Seven presidential candidates were in the race but the BBC’s Will Ross in the capital Accra says that the other candidates failed to attract much support.
He says the winner could get more than 50% of the vote, making any second round run-off later this month unnecessary.
There is little love lost between the two main political parties, our correspondent says.
The governing NPP dominated the outgoing parliament with 128 of the 230 seats.
‘Good day for Africa’
Parliamentary results so far show the centre-right party has lost at least half a dozen seats to the NDC, including that of President Kufuor’s information minister.
Initial results show that a third contender who was tipped as a potential kingmaker or spoiler has performed poorly, increasing the chance of a first-round win for one of the frontrunners.
Papa Kwesi Nduom, candidate for the Convention People’s Party, which ushered in Ghana’s independence from Britain half a century ago, had hoped to spring a surprise.
The vote appeared free of the intimidation and violence that have marred other recent African polls, according to local and international observers.
Baroness Valerie Amos, a former British minister who is leading a 23-nation Commonwealth observer mission, said Sunday had been “a good day for Africa”.
Our correspondent say this election is important not just for Ghana, but also for the continent, where bloodshed and claims of fraud have dogged polls from Kenya to Zimbabwe and Nigeria.
The fact that the hallmark for a successful election is that it is peaceful is seen by some as a worrying sign of just how low the bar has been set when it comes to judging democracy in Africa, he adds.
Ghana was the first African state to gain its independence in 1957, but was plagued by coups until the return to multi-party democracy in 1992.
It is the world’s second biggest cocoa grower and Africa’s number two gold miner.