John Simpson in Lagos: Ballot rigging may have been intended to make up for the low turnout

But his rival, Olu Falae, has rejected the result of the vote, accusing Mr Obasanjo's supporters of "monumental" vote-rigging.

Former United States President Jimmy Carter, who is in Nigeria as an election observer, also questioned the outcome of the poll.

Mr Obasanjo, who is a former military ruler, received nearly twice as many votes as Mr Falae.

He promised that the cause of democracy would be advanced under his presidency.

Nigeria's independent National Electoral Commission said Mr Obasanjo had receieved 18.7 million votes, against Mr Falae's 11.1 million.

'Pattern of malpractice'

Mr Falae issued a statement that alleged a "seemingly institutionalised pattern of election malpractices" in the presidential poll.

The former finance minister and his electoral partner, Umaru Shinkafi, issued the statement just before the results were announced, in an unsuccessful attempt to stop the poll from being accepted.

Jeremy Vine in Lagos: "Democracy is sending a thrill through Nigeria"

Mr Falae, who was standing jointly for the Alliance for Democracy and the All Peoples Party, said it was too early to say whether he would challenge the results in court.

Carter questions result

Mark Doyle: Carter statements could cause confusion

Mr Carter told the electoral commission that it was impossible to make an accurate judgement about the outcome of the election.

He pointed to a "wide disparity between the number of voters observed at the polling stations, and the final result that has been reported from several states".

But most observers were of the view that although there had been malpractices, the size of Mr Obasanjo's lead meant that his victory was not in question.

There was particular concern over ballot-rigging by both sides in the economically deprived Niger Delta region.

Why a soldier?

BBC West Africa Correspondent Mark Doyle says one of the key questions about the election is why the big political power-brokers of Nigeria decided to put up a retired military man as their candidate.

Some say Mr Obasanjo is there to protect the military from corruption investigations, while others say he is the man who may be able to stop the soldiers seizing power again in the future.

Both presidential candidates voted in their home towns on Saturday, expressing hope that the election would bury military rule.

Falae support in south-west

General Obasanjo swept to victory in northern, central and eastern Nigeria. Chief Falae - as expected - did well in the south-west.

The general's Peoples' Democratic Party (PDP) widened its lead by several percentage points compared to recent local, state and parliamentary elections in which it secured a majority of the vote.

Ready to govern

General Obasanjo's supporters have been celebrating and are already looking forward to government. Nigeria's current military ruler, General Abdulsalami Abubakar, has pledged to step down on 29 May, to make way for civilian rule.