Ruling party candidate Bola Tinubu has been declared the winner, getting 37% of the vote
He got the most votes nationwide and met the requirement of at least 25% ballots cast in two-thirds of Nigeria's 36 states and the capital
His main rival Atiku Abubakar polled 29%, and Labour's Peter Obi 25%
Three opposition parties allege widespread rigging, calling it a sham election
Earlier, ex-President Obasanjo issued a warning about the poll results
The candidate of the opposition PDP party, Atiku Abubakar, has won the presidential race in Yobe state, according to official results.
He got 198,567 votes compared to Bola Tinubu's 151,459 from the APC. Labour's Peter Obi trailed with 2,406 votes.
Nigeria's ruling party candidate has won Oyo state in his south-west stronghold by a landslide, official results say.
He got 449,884 votes, compared to the 182,977 of his main rival Atiku Abubakar and the 99,110 of Labour's Peter Obi.
The ruling party's candidate, Bola Tinubu, has won in south-western Ogun state by a wide margin, official results show
He got 341,554 votes. The main opposition candidate, Atiku Abubakar, got 123,831 and Labour's Peter Obi 85,829.
Nigeria's main opposition candidate, Atiku Abubakar, has won the presidential race in southern Akwa Ibom state, according to provisional results announced by election officials in the state.
Mr Abubakar won 214,012 votes. He was trailed by the ruling party's Bola Tinubu, who got 160,620 votes. Labour's Peter Obi came third, with 132,683 votes.
Joshua Ajayi
BBC News, Abuja
An agent of Nigeria's Labour Party has warned that it will not accept any of the presidential election results if the election commission does not upload them on its online portal, before announcing them at its headquarters in the capital Abuja.
Labour's candidate is Peter Obi, who is contesting the presidential poll for the first time.
Agents of four other parties - including the main opposition PDP - have expressed a similar view.
However, a representative of the ruling APC has disagreed with them, saying the process should continue and Nigeria's constitution provides for results to be contested at election petition tribunals.
To be declared a winner in Nigeria's presidential election, a candidate needs to have the most votes and a quarter of ballots cast in 25 of the 36 states plus Abuja.
This is intended to ensure that the new president has reasonable support across the country.
Nigeria is Africa's most populous country, with a population of more than 200 million.
The election is being contested by 18 candidates, with three frontrunners - the ruling party's Bola Tinubu, the main opposition's Atiku Abubakar, and the small Labour Party's Peter Obi.
Provisional results are coming in from each state, but they become official only after they are confirmed by the head of the Independent National Electoral Commission (Inec), Mahmood Yakubu
Yemisi Adegoke
BBC News, Yola, Adamawa state
Main opposition candidate Atiku Abubakar has comfortably won the presidential election in his home state of Adamawa, according to provisional results from state election officials.
Mr Abubakar got 417,611 votes; his closest rival Bola Tinubu 182,881.
Labour's Peter Obi came third, with a better than expected 105,648 votes.
Cousins Chidera and Onyinye's dream to vote in their first-ever presidential election in Nigeria was cut short by a disturbance.
Read MoreBina Jennifer Efidi was hit with a sharp object while she was waiting to vote in Lagos.
Read MoreBola Tinubu's campaign team has issued a statement after provisional results showed that he had lost Lagos - the state with the most registered voters - to Peter Obi.
He appealed to the people of Lagos to be calm and to "eschew any act that can lead to breakdown of law and order", the statement quoted him as saying.
Mr Tinubu believed that "the beauty of democracy is that people have a right to vote for the candidate of their choice", and as "a democrat he is bound to accept the outcome of any election whether favourable or not", the statement added.
Image source, AFPThe army was deployed on election day to keep the peace
An aide of Nigeria's President Muhammadu Buhari has quoted the ruling party's candidate, Bola Tinubu, as urging his supporters to stay calm after provisional results showed that he had lost Lagos - the biggest state - to Peter Obi.
Quoting Mr Tinubu, Bashir Ahmad said on Twitter: "The fact that the APC narrowly lost Lagos state to another party should not be the reason for violence. As a democrat, you win some, you lose some."
Mr Tinubu has historically been seen as a powerful figure in Lagos and was once its governor.
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Analysis
Akinyemi Akinrujomu
BBC News, Lagos
The presidential candidate of Nigeria's ruling APC party, Bola Tinubu, won in all 16 local government areas in Kwara state in Saturday’s election.
Mr Tinubu polled 263,572 votes to defeat his closest challenger and the candidate of the PDP, Atiku Abubakar, who polled 136,909 votes, while Peter Obi of Labour and Rabiu Musa Kwankwaso of the NNPP garnered 31,166 and 3,141 votes respectively.
Mr Tinubu’s victory in Kwara, which has a large population from his Yoruba ethnic group, not only brightens the chances of his camp, but it has also raised questions about whether the so-called Kwara-portent will favour him.
Historically, since Nigeria’s return to democratic rule in 1999, whichever candidate wins in Kwara has gone on to win the presidency.
Former Presidents Olusegun Obasanjo, Goodluck Jonathan, Umar Musa Yar’Adua and even current President Muhammadu Buhari all won in Kwara.
The electoral umpire in Nigeria, the Independent National Electoral Commission (Inec), has officially begun announcing the results coming in from across the country.
It is still too early to tell how results will play out for Mr Tinubu.
Nduka Orjinmo
BBC News, Abuja
Official results in so far from Nigeria's presidential election show that ruling party candidate Bola Tinubu is dominating in his strongholds in the south-west.
He has won three states in the region, while marginally losing a fourth to main opposition candidate Atiku Abubakar.
But delays in getting results from 32 other states and the capital, Abuja, has led to growing frustration.
The electoral commission has apologised for the unresponsiveness of its results viewing page on its website, saying that a surge in usage caused technical hitches.
Joshua Ajayi
BBC News, Abuja
Mild drama ensued during the official announcement of results at the election commission headquarters in the capital, Abuja.
Tensions rose before the beginning of the collation of results when the agent of the main opposition party, the Peoples Democratic Party (PDP), said that the figures announced for Ekiti state do not add up.
The commission had declared the presidential candidate of the ruling All Progressives Congress, Bola Tinubu, the winner in Ekiti with 201,494 votes, defeating his closest rival Abubakar Atiku of the PDP with 89,554.
Peter Obi of Labour got 11,397 votes while the candidate of the New Nigeria Peoples Party (NNPP), Rabiu Kwankwaso, polled 264 votes.
The PDP agent, Dino Melaye, said his party had observed a discrepancy - an increase of 887 votes in the total number of figures from Ekiti.
The agents of two other political parties - Action Alliance and Labour - agreed with Mr Maleye.
The election commission chairman, Mahmood Yakubu, insisted that the commission stood by the result declared for Ekiti.
This did not stop Mr Melaye, who continued his outburst and almost stopped the collation of results for another state, Kwara, which has been won by Mr Tinubu.
Nigeria's Independent National Electoral Commission (Inec) has so far announced the results of four states at its headquarters in the capital, Abuja.
The winners in each state are as follows:
However, there were dramatic scenes during the announcement as the PDP, Action Alliance and the ADC rejected the Ekiti results, alleging overvoting.
We also have provisional results from other states, including Lagos, the biggest state in Nigeria.
The provisional results show that Peter Obi from the Labour Party has won the state. This is a huge setback for Mr Tinubu, who fought hard for the state and was its governor from 1999 to 2007.
Provisinal results also show that Mr Abubakar has won in Katsina, from where outgoing President Muhammadu Buhari comes. He is a member of the APC, and backed Mr Tinubu in the election.
Inec is currently taking a break and will be back within the hour.
The presidential candidate of Nigeria's ruling APC party, Bola Tinubu, has won in south-western Ondo state by a wide margin, official results show.
He got 369,924 compared to the 115,463 of his closest rival, Atiku Abubakar. Peter Obi got 47,350.
Nigeria's opposition PDP candidate Atiku Abubakar has won the presidential poll in south-western Osun state with 354,366 votes, official results show.
The ruling party's Bola Tinubu got 343,366.
Mr Abubakar's victory is not surprising, as the state governor was elected on a PDP ticket.
Nigeria's ruling party candidate Bola Tinubu has won the presidential election in his stronghold of Oyo state in the south-west, according to provisional results announced by election officials in the state.
He got 449,884 votes, compared to Atiku Abubakar's 182,977 and Peter Obi's 99,110.
Nigeria's ruling party candidate Bola Tinubu has won the presidential election in central Kwara state, official results show.
He got 263,572 votes to the 136,909 of his nearest rival, Atiku Abubakar.
Labour's Peter Obi got 31,186 votes.
Joshua Ajayi
BBC News, Abuja
Image source, Getty ImagesBola Tinubu is referred to as the political "godfather" of the south-west
Party agents of the Nigeria's opposition PDP and Labour are contesting the results of south-western Ekiti state, saying there was over-voting.
Official results showed the state was won by ruling party candidate Bola Tinubu. Ekiti is seen as one of his strongholds.