Abubakar, who was deputy to Olusegun Obasanjo from 1999 to 2007, said Buhari's All Progressives Congress had failed to deliver the change it promised before coming to power in 2015.
Instead, it had become as factionalised as its rivals, he said, accusing it of a "draconian clampdown on all forms of democracy within the party and the government it produced".
"The party we put in place has failed and continues to fail our people, especially our young people," Abubakar -- 71 on Saturday -- said in a statement.
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"A party that does not take the youth into account is a dying party.
"I admit that I and others who accepted the invitation to join the APC were eager to make positive changes for our country that we fell for a mirage...
"After due consultation with my God, my family, my supporters and the Nigerian people... I, Atiku Abubakar... hereby tender my resignation from the All Progressives Congress while I take time to ponder my future."
Abubakar is widely expected to rejoin the Peoples Democratic Party (PDP) in a bid to become its candidate for the next elections due on February 16, 2019.
The Daily Trust newspaper said in an online report he would formally collect his PDP membership card in his home state of Adamawa, in northeast Nigeria, on Saturday.
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The former vice-president, who has sought the country's top job at elections dating back to 1993, was one of a number of PDP members who quit the party before the last vote.
The exodus was prompted by the reported refusal of the then-president Goodluck Jonathan -- a southern Christian -- to step down for a candidate from the Muslim majority north.
The PDP has said its presidential candidate will be from the north this time round. Buhari, 74, is also from the north.
Only one PDP lawmaker -- Peter Ayodele Fayose, governor of the southwestern state of Ekiti -- has so far declared his intention to run.
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