By PATRICK MCGROARTY in Lagos, Nigeria, and HEIDI VOGT in Yola, Nigeria
Updated March 31, 2015 1:47 p.m. ET
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Former military dictator Muhammadu Buhari won Nigeria’s presidential elections, an unprecedented rebuke to a political class that many voters said had squandered oil riches while development languished and insurgency spread.

With just one state left to report, Nigeria’s election commission said Mr. Buhari had won 53% of 29 million votes cast over the weekend. President Goodluck Jonathan, the first incumbent to lose an election since democracy returned to Nigeria in 1999, won 46%.

Mr. Jonathan called Mr. Buhari to concede, an adviser to the president said. Both candidates pledged to respect the results, if they are deemed credible.

But early Tuesday, a representative from Mr. Jonathan’s party alleged Nigeria’s electoral commission was favoring Mr. Buhari’s party.

Peter Godsday Orubebe of the ruling People’s Democratic Party said he wanted the results thrown out in a number of northern states that backed Mr. Buhari overwhelmingly.

He also accused the commission of investigating reports of voting irregularities in states Mr. Buhari hoped to win, but not northern Buhari strongholds where Mr. Jonathan’s party has cried foul.

“We have lost confidence in the process,” he said.

Nigerians vote in a presidential election on March 28. WSJ looks at the key players, the threat of Boko Haram and what the result could mean for a country that has been beset by corruption.
Mr. Buhari’s party decried the voting process in the southeastern Rivers State, a bedrock of Mr. Jonathan’s support. The governor there, one of Mr. Buhari’s campaign managers, alleged intimidation by security forces and breakdowns in the voting process—and sought to cancel the vote in that state.

Nigerian Election Commission Chairman Attahiru Jega said the disruptions weren't enough to discredit the overall vote. “Elections all over aren’t perfect but we don't see grounds substantial enough to cancel the entire result.”

More than 50 million people were accredited to vote in Nigeria’s chaotic and occasionally violent elections this weekend. The vote was extended to Sunday after the failure of some new voter-identification equipment.

Although election observers were mostly positive about the vote despite technical problems, the U.S. and U.K. on Monday warned of efforts to manipulate the results, the latest troubling sign in a country with a history of post election violence.

“We have been receiving numerous and credible reports from around the country from people concerned about the voting process,” a State Department official said.

Mr. Buhari now will have to try to revive an economy—the biggest in Africa—hit hard by the crumbling price of oil, Nigeria’s main export and source of government revenue. Fitch Ratings put Nigeria’s government debt on negative outlook on Monday, a sign a downgrade could be imminent. Standard & Poor’s Ratings Services downgraded Nigeria’s debt this month.

Mr. Buhari, who led the country for 20 months after a 1983 coup, has pledged to plug budget holes by tackling corruption.

Mr. Jonathan, a 57-year-old former zoology professor, had said he would cut spending to protect the government’s balance sheet.

Economists say either approach would collide with Nigeria’s entrenched political class and face long odds.