According to official results, the 70-year-old political veteran won 36% of the vote. His main rival, Atiku Abubakar, won 29% of the vote and Peter Obi, from the Labor Party, 25%.
Both considered the voting process a farce and demanded a repetition.
Tinubu, one of Nigeria's richest politicians, based his campaign on his record of rebuilding the largest city, Lagos, when he was its governor.
However, he was defeated in the city by Obi, a newcomer who mobilized the support of many young people, especially in urban areas, undermining the country's two-party system.
Bola Tinubu, with his campaign entitled "It's my turn", won most of the other states, where he is known as a "political godfather".
Current President Muhammadu Buhari will step down after two terms marked by economic stagnation and growing insecurity across the country - from an Islamist insurgency in the northeast to a national crisis of kidnappings for ransom and separatist attacks in the southeast.
