The postponement comes just hours before polls were due to open in Africa's most populous country.
"Following a careful review of the implementation of its logistics and operational plan and the determination to conduct free, fair and credible elections, the Commission came to the conclusion that proceeding with the elections as scheduled is no longer feasible," INEC said in a statement.
The statement added that "consequently, the commission has decided to reschedule the Presidential and National Assembly Elections to Saturday, 23rd February 2019. Furthermore, the Governorship, State House of Assembly and Federal Capital Territory (FCT) Area Council Elections is rescheduled to Saturday, 9th March 2019.
"This will afford the Commission the opportunity to address identified challenges in order to maintain the quality of our elections."
The electoral watchdog said the decision to postpone the vote was a difficult one to take.
"This was a difficult decision for the Commission to take, but necessary for the successful delivery of the elections and the consolidation of our democracy.
"The Commission will meet key stakeholders to update them on this development at 2pm on Saturday, 16th February, 2019 at the Abuja International Conference Center."
Suggestions that the election will be postponed emerged a little before midnight of Friday, February 15, 2019 when it became clear that ballot materials were yet to arrive a couple of States, including Niger and Ekiti, Pulse Nigeria reports.
Meanwhile, the two main political parties swiftly condemned the move and accused each other of orchestrating the delay as a way of manipulating the vote.
Voting had been due to start at nearly 120,000 polling stations in Africa's most populous nation at 0700 GMT, with a record 73 candidates on the ballot.
President Muhammadu Buhari, 76, was set to seek a second term of office against a stiff challenge from the main opposition candidate, former vice president Atiku Abubakar, 72.
Buhari's campaign spokesman Festus Keyamo, for the ruling All Progressives Congress, (APC) said the news was a "huge disappointment" and hit out at INEC for being unprepared.
Keyamo called on the body to remain impartial "as the rumour mill is agog with the suggestion that this postponement has been orchestrated in collusion with the... PDP".
For his part, Abubakar of the main opposition Peoples Democratic Party blamed the Buhari government for "instigating the postponement" but called on his supporters to remain calm.
"We will overcome this. You can postpone an election but you cannot postpone destiny," he added in a statement.
About 84 million Nigerians registered to vote in the 2019 elections, a 25 percent increase from 2015. 51 percent of registered voters are young people, aged 18 to 35 years.