Bola Tinubu of the ruling APC party and former Vice President Atiku Abubakar of the People’s Democratic Party are seen as having the best chance of winning.
Labour-Party candidate Peter Obi is also expected to do well.
In Africa's most densely populated country with a total of 220 million people, 87 million are eligible to vote.
The elections are taking place under tight security measures. Armed militias are active in some parts of the country, including the jihadist Boko Haram.
Nigeria's borders will be closed on election day and, with a few exceptions, cars will not be allowed to drive either.