President-elect Muhammadu Buhari on Wednesday vowed to rid Nigeria of "terror" after his historic election victory marking the first democratic transfer of power in Africa’s most populous nation.

President-elect Muhammadu Buhari on Wednesday vowed to rid Nigeria of "terror" after his historic election victory marking the first democratic transfer of power in Africa's most populous nation.

The 72-year-old former military ruler also pledged reconciliation with political opponents who fear a return to his autocrat regime of the 1980s, and a government representing "all Nigerians".

"I assure you that Boko Haram will soon know the strength of our collective will and commitment to rid this nation of terror and bring back peace," he said in an acceptance speech after his dramatic win.

"We shall spare no effort until we defeat terrorism."

Boko Haram, whose rampage through northeastern Nigeria has left more than 13,000 people dead in six years, is Buhari's most pressing security problem.

He also promised to address a culture of political impunity and the "evil" of rampant corruption but said there would be no witch-hunt and his beaten opponent Goodluck Jonathan had "nothing to fear".

"Our long night has passed and the daylight of new democratic government has broken across the land. Democracy and the rule of law will be established in the land.

"Let's put the past behind us, especially the recent past. We must forget our old battles and past grievances and forge ahead."