Buhari won with 3,430 votes while Atiku came third with 954.
Kano State Govenor, Rabiu Musa Kwankwaso, was second with 974 votes.
In a concession statement by his media office in Lagos on Thursday, Atiku said Buhari ran a spirited campaign and that since the delegates have spoken, he fully deserves the victory.
“I am very confident that you will provide the needed leadership to turn this country around. I have no doubt that you will work with dedicated and qualified Nigerians to protect our citizens, improve our economy, create jobs, improve education, reform governance and fight corruption. You will indeed bring the change Nigerians have been yearning for. Once more, congratulations.
“I congratulate the other contestants, namely Governors Rabiu Musa Kwankwaso and Rochas Okorocha as well as the erudite Sam Nda-Isaiah. You have all demonstrated your commitment to democracy by participating in this transparent process and by campaigning vigorously across this country.
“I thank our delegates for their sacrifices and their commitment to democracy. In particular, I thank those who voted for me for your faith in me. However, since we came up short, we have to now rally behind General Buhari to help him prevail in the coming Presidential election.
“The APC has demonstrated, through the transparent process, the Party’s commitment to democracy and rule of law. It has demonstrated its respect for people and their choice through the ballot box.
“I sincerely thank the Convention Committee for putting together a hitch-free convention.
“My dear friends, we have voted, a winner has emerged. I pledge my commitment to this Party, and to campaign vigorously for our candidate, Gen. Muhammadu Buhari and all APC candidates to ensure victory in the 2015 elections.
“I call on all other contestants and our party’s rank and file to unite behind our candidates at all levels to ensure that the PDP is defeated, so Nigerians can have real change.
“I will hand over to Gen. Buhari for his review and possible implementation my policy document which was developed in line with the party’s philosophy.
“Long live APC!
“Long live the Federal Republic of Nigeria!
“Thank you all and God bless!”