Over 300 legislators are also due to be elected to the country's Senate and House of Representatives.
Today's poll is by no means orderly, with the Abuja attack on the country's electoral commission the most high-profile demonstration of Nigeria's ongoing stability.
A lorry laden with fuel and gas cylinders was driven towards the headquarters by an attacker, who flung himself from the vehicle after pressing down the accelerator with a rock.
His efforts were in vain, however, as the lorry came to a stop before reaching its target and did not explode.
Elsewhere in Nigeria, especially in the southern coastal cities of Lagos and Port Harcourt, delayed delivery of ballot papers has left many polling stations without the materials necessary to process the poll.
Popular fears of fraud and rigging are widespread while sporadic violence is being reported in the country's rural areas.
Up to 65 million people are eligible to vote in the country's 120,000 ballot boxes.
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