Buhari's All Progressives Congress (APC) opposition party declared victory and celebrations began among party grandees in the capital, Abuja.
If confirmed, it would be the first democratic change of power in the history of Africa's most populous country and cap a remarkable return for the 72-year-old who headed a military regime in the 1980s.
With 34 out of 37 results in, the APC had won 19 states, while Jonathan's Peoples Democratic Party (PDP) was on 14, plus the Federal Capital Territory of Abuja.
Buhari was more than 2.75 million votes ahead of 57-year-old Jonathan, after winning Yobe and Adamawa, which have been among the hardest hit by the bloody, six-year Boko Haram insurgency.
Also Read
The retired army general won the key prize of Lagos in the southwest but at one point his lead was cut to 500,000 votes after landslide victories for Jonathan in his southern Delta homeland.
The vote was the closest election contest ever in Africa's biggest economy which has a population of 173 million.
There was a brief protest by Jonathan's PDP before the count resumed today.
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."
In Kano, Buhari defeated Jonathan by nearly 1.7 million votes after besting the president by roughly one million in 2011.