Despite violence linked to Boko Haram militants and sporadic unrest elsewhere, UN chief Ban Ki-moon and others praised the conduct of the vote and called for calm to avoid a repeat of deadly rioting that followed 2011 elections.
In a sign of the continuing threat posed by the Islamists however, military fighter jets and ground troops pounded Boko Haram fighters in the northeastern state of Bauchi after a series of attacks on polling stations at the weekend.
The presidential election in Africa's most populous nation and largest oil producer is the closest in the country's history, with the first credible challenge from an opposition party.
Jonathan's Peoples Democratic Party (PDP) has been in power since Nigeria returned to civilian rule in 1999 but is being pushed to the wire by main opposition candidate Buhari.
First results could be given from today, the head of the country's electoral commission, Attahiru Jega, said last night.
The prospect of a democratic transfer of power - plus economic woes caused by the slump in global oil prices, concerns about corruption and fears about insecurity - served to energise the vote.
One government spokesman claimed there was a "record turnout" and voting was largely peaceful despite pockets of unrest mainly in southern states such as the key battleground of Rivers.
The technical difficulties of the voting process, however, set the tone for a potential dispute as the PDP has opposed the use of handheld electronic devices to authenticate voters, saying they were not sufficiently tested.
Buhari's All Progressives Congress (APC) supports the new system as a means of curbing the voter fraud that has marred previous elections.
Jega told a news conference yesterday the electoral commission was confident its objective of holding a "free, fair, credible and peaceful" election was "on course".
"We appeal to all Nigerians to remain peaceful as they await the return of these results," he added, with fears of a repeat of 2011 post-poll violence that left some 1,000 people dead.
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