"Polling stations have opened. Accreditation has started," Independent National Electoral Commission spokesman Kayode Idowu told AFP, despite reports of delays to the 8:00 am (1230 IST) start.
Reporters said the process had not started at some locations in Kano, Lagos and Abuja because of the late arrival of INEC officials and election materials. Voting proper is due to start at 1:30 pm local time.
President Goodluck Jonathan is seeking a second four-year term as leader of Africa's most populous nation against a strong challenge from the main opposition candidate Muhammadu Buhari.
Buhari, a former military ruler who has a reputation for fighting corruption, also charges that Jonathan has done little to tackle rampant graft in government, particularly in the oil and gas sector.
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The election was postponed from February 14 because of military operations against Boko Haram in the northeast, which has since seen a series of claimed successes against the militants.
Many people had formed queues outside polling stations since the early hours or even slept overnight.
The Muslim-majority north is generally seen as a stronghold of Buhari and his All Progressives Congress (APC) opposition.
Jonathan and his Peoples Democratic Party (PDP) are viewed as having larger support in the mainly Christian south.
In the president's home town of Utuoke, Bayelsa state, Laurence Banigo, a 42-year-old civil engineer, said: "This is a great day for our son, and we are set to return him to power.
"He has done well. He deserves a second term."
"We are ready 100 per cent to vote, to vote the candidate that will protect our lives and integrity of this country," he said.