While the All Progressives Congress polled 87 votes in the presidential election, the People's Democratic Party got just 18 votes.
Obasanjo had picked Atiku over Buhari, advising the president to quit politics.
Northeast Nigeria has been hit by the decade-long Boko Haram insurgency with attacks in recent months carried out by offshoot Islamic State in West Africa Province. "We do not want any hanky panky", he said.
President Buhari was one of the first in the queue when the almost 120,000 polling stations began opening at 0700 GMT. "I'm going to be the victor", he told reporters.
Some Nigerians are reporting low turnout or the late opening of polls more than one hour into the presidential election.
The results from Mr Abubakar's polling unit are amongst some of the early returns trickling in from across the country in today's presidential and federal parliamentary elections.
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Domestic and worldwide observers to the Nigerian presidential elections were present at polling stations in Yola and Abuja.
"Logistics weren't properly managed despite the postponement of the polls", said Idayat Hassan, director of Abuja-based think tank Centre for Democracy and Development, which is also observing the election.
"Before dealing with migration, we have to deal with freedom in a country", she said, adding that migration "is the last thing we have to talk about".
The president "has failed", said David Ojo, a barber in Danbatta in northern Kano state who joined excited voters in supporting Buhari in 2015. "I need my salary to increase".
Boko Haram has warned it will disrupt the elections.
"Owing to the sound of heavy gunfire heard this morning around Maiduguri Metropolis, the Commissioner of Police Borno State, CP Damian Chukwu wishes to inform members of the public that there's no attack on any part of Maiduguri and hence no threat to public peace and order", Edet Okon, spokesman of the Borno police command, said in a statement. Shettima's motorcade was attacked by insurgents on 12 February on route to an election rally.