Omar died in Pakistan in April 2013, the office of Afghan President Ashraf Ghani said in Kabul, citing "credible information".
It didn't specify a cause or say why the news was being revealed only now.
The Afghan Taliban issued a statement last night saying they were "not aware" of a new round of peace talks that had been expected to take place in Pakistan today. It appears to indicate they will not participate in the second round of the official face-to-face talks with the Afghan Government.
It was not clear if they were pulling out of the talks, which began this month.
Taliban factions disagree on whether to pursue the peace process, particularly as the group has lost local commanders to Isis (Islamic State).
"The absence of Mullah Omar is further splintering the Taliban, and that's bad news for peace talks," said a senior analyst at the International Crisis Group in Kabul, Graeme Smith.
"Kabul wants to negotiate with a single large opponent, and trying to haggle out deals with smaller factions would be harder. It's also opening the door for other militant groups, such as self-declared Islamic State factions, which are less willing to negotiate."
The Taliban are planning to formally announce the death of Omar and declare his son Mohammad Yaqub as his successor and the organisation's leader, a Taliban commander in the nation's southern Helmand province, Mullah Akhtar Mohammad, said yesterday.
Omar's deputy, Akhtar Mohammad Mansoor, opposes the family succession because the son has not supported recent peace talks with the Government, the commander said. Omar's deputy did endorse the talks, he said.
The first formal discussions between the Taliban and the Afghan Government since 2001 occurred in the Pakistani hill town of Murree early this month.
They raised hopes for a political solution to a conflict that has killed almost 100,000 people since 2001.
The involvement of Pakistan, which has close ties with the Taliban leadership, appeared to signal a new level of seriousness to peace efforts.
