He said Atiku polled 1,532 votes while Aminu Tambuwal polled 693 votes to place second.
He will be running against President Muhammadu Buhari, who is the candidate of ruling All Progressives Congress (APC), in the 2019 presidential election.
"On behalf of al of us, we congratulate you".
Abubakar hopes to replicate Buhari's 2015 feat of winning a presidential election at the fourth attempt after he left the ruling APC party in November and re-joined the PDP a month later. That is to say, we will all work for the development of the country.
"This is a victory for all of us".
Abubakar also beat 10 other aspirants including Senate President Bukola Saraki and Rabiu Kwankwaso, ex-governor of Kano, to clinch the opposition party's ticket.
"We are with you and confident that with us as a team May 29 2019 will be a day that our party will take over". His spokesperson had earlier confirmed that the Twitter handle belongs to his principal.
"I can not do it alone, I need your support, your assistance, I need your understanding and I need your participation".
"Under his tutelage, I learnt quite a lot and I believe the experience and care I got is going to definitely impact on how we eventually govern this country, I wish to pay my personal tribute to him", he added.
He described the process that produced him candidate as free, fair and innovative.
In his acceptance speech, Mr Abubakar praised the conduct of the primary as the best since the enthronement of democracy in 1999.
Mr Abubakar, who spoke without a prepared script, commended his challengers, saying they showed "a sense of unity, a sense of objective and a sense of commitment". The party must elect a candidate that can effective combine our strength to win the 2019 election, " he said.
"We invite the whole world to note that the PDP conducted its presidential primary and a clear victor, Atiku Abubakar, emerged, without any form of disagreements or reliance on heavy security".