Commission chairman Attahiru Jega said Buhari received 15.4 million votes to Jonathan`s 12.9 million.
Late Tuesday when the outcome of the election was apparent, Nigerian President Goodluck Jonathan conceded defeat, thanking all Nigerians for the opportunity to lead them.
Jonathan said he kept his promise for a free and fair election and appealed to those who disagree with the outcome to follow due process under the constitution and election laws.
Jonathan, whose party ruled the country for 16 years, said his supporters should celebrating "a legacy of democratic freedom, transparency, economic growth, and free and fair elections."
Though Jonathan, 57, took advantage of a six-week postponement in the vote to campaign hard, Nigerians appeared to be angry about his government`s failure to stop attacks by the Boko Haram militants, as well as a sputtering economy and endemic corruption.
Buhari, 72, was previously the country`s military ruler for 20 months after officers seized power in a 1983 coup. He was toppled by another military coup, but has run for the presidency four times since democracy was restored in Nigeria in 1999.
He will be inaugurated May 29.
Buhari also won at least 25 percent of the vote in at least 24 states, as required under the constitution.
Yau Shehu Darazo, a top aide to Buhari, said Jonathan had called his rival to congratulate him. Officials from both Buhari`s party and Jonathan`s party also confirmed to VOA that Buhari had accepted Jonathan`s concession.
The result marks the first time in Nigeria`s history that an incumbent president was ousted at the ballot box and also heralds the end of a 16-year rule of Jonathan`s Peoples Democratic Party.
Some victories in south
Some of Buhari`s victories came in states in southern Nigeria, which is generally considered a stronghold for Jonathan.
Tensions persisted in Port Harcourt, in the oil-rich Niger Delta region, where officials declared a dusk-to-dawn curfew. Rivers state has been the scene of some post-election protests.
The All Progressives Congress has called for the election there to be redone after alleged vote-rigging.
Jega, however, said Tuesday that commission investigators found no "substantial grounds" to cancel the vote there.
Post-election violence marred the country`s disputed 2011 vote, resulting in about 800 deaths, mostly in the nation`s northern regions.
On Monday, U.S. Secretary of State John Kerry and British Foreign Secretary Philip Hammond released a joint statement saying there were "disturbing indications" that the collation process "may be subject to deliberate political interference."
`Acceptable` Voting
International observer missions had called the conduct of the voting "acceptable," despite technical glitches in a new computerized, anti-fraud system that prompted officials to extend voting by a day.
Nigerians across the country appeared to be closely watching the commission`s work, broadcast live on national TV.
"There’s tension right now in Lagos because people are anxious to have the results. People are anxious," said David Olayemi, a Lagos resident. "They are waiting for the results, for the announcement of the new elected president."
In the northern city of Kano, where men sat drinking tea and listening to a radio, Abdul Rashid Sani said he suspected the government was up to something. He said the results from previous elections came faster, but he was confident that his party, the All Progressives Congress, will win.
In Kaduna, Al Amin Jinge also voiced concerns about the outcome.
"Everybody is afraid of the announcement of result. That’s why everybody hide at home," he said. "But we pray so nothing will happen, that, God willing, there is not any violence."
Nigeria`s election originally was scheduled for mid-February, but officials pushed back the vote because of fighting and instability in northeastern states where Boko Haram militants have been battling the government since 2009.
The security situation improved after a multinational offensive drove the militants from many towns they had controlled.
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