The former Nigerian military ruler led by more than 3 million votes late on Tuesday, with results in from 35 out of 36 states, plus the capital Abuja.
Jonathan had closed Buhari’s lead since Monday night by claiming, as expected, the key oil-producing state of Rivers by a landslide.
However, multiple reports have indicated that Jonathan called Buhari to congratulate him on the victory.
The final election result and official declaration of Buhari as winner is expected to be announced later this evening.
Saturday’s election spilled over into a second day of voting following glitches with some electronic card readers, which were introduced to help prevent electoral fraud.
There were also security fears in some areas, with an electoral headquarters in oil-producing Rivers State burned down. Some regions saw protests over alleged killing of opposition workers and voting irregularities, but fears that the Boko Haram insurgency would try to disrupt the election did not come to pass.
Jonathan is head of the Peoples Democratic Party (PDP), while Buhari heads the All Progrssive Congress (APC). The pair last week signed an agreement aimed at preventing any violence during voting, a hallmark of previous elections. That deal was brokered by ex-military ruler Abdulsalami Abubakar.
Nigeria sealed off its land and sea borders in an effort to hold a free and fair election and an attempt to impose strict security measures during voting time.
Saturday’s poll was originally set for 14 February but was delayed in order to allow the country to guarantee a greater degree of security amid the ever-present threat from Islamic militant group Boko Haram.