If confirmed, it would be the first democratic change of power in the history of Africa's most populous country.
With 32 out of 37 results in, Buhari's All Progressives Congress (APC) had won 19 states with Jonathan's Peoples Democratic Party (PDP) on 12 plus the Federal Capital Territory of Abuja.
Asked if the APC was claiming victory over the PDP, party spokesman Lai Mohammed told AFP: "Yes.
"This is the first time the opposition has voted a government out of power in Nigeria's history," he added.
They included the northeastern states hit hardest by the six-year Boko Haram insurgency.
The former military ruler won the key prize of Lagos in the southwest but at one point his lead was cut to 5,00,000 votes after landslide victories for Jonathan in his southern Delta homeland.
The vote pitting Jonathan against Buhari was the closest election contest ever in Africa's biggest economy which has a population of 173 million.
The opposition leader, making his fourth run at the presidency, has been buoyed by frustration over endemic corruption, criticism over Jonathan's handling of Boko Haram and a stronger opposition.
Former Niger Delta minister Godsday Orubebe accused elections chief Attahiru Jega of being "partial" and "selective".
Orubebe claimed Jega had refused to investigate PDP complaints about big wins by Buhari in northern states but had launched a probe into claims by the APC of irregularities in Rivers.
Jega said later: "I don't believe that the allegations are substantial enough to require the cancellation or rescheduling of the elections in Rivers state. We will take the results."
But Buhari -- who ruled from December 1983 to August 1985 -- encouraged by tallies from two northern states, where he stretched his lead over Jonathan compared to four years ago.
And in Kaduna, where the two ran neck-and-neck in 2011, Buhari won by 650,000 votes.
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