In a statement released on Thursday, the Afghan Taliban said Mullah Omar had died from disease.
The statement did not provide details about the time and location of his death, nor did it give out details of his successor.
However media reports are suggesting that his deputy, Mullah Akhtar Mansour, is to replace the former Taliban leader.
In light of the news of Omar's death, a second round of meetings between Taliban representatives and the Kabul government has been postponed.
The talks were previously scheduled for today.
Mohammad Nateqi, an Afghan political analyst, says the death of Omar will likely deepen Taliban divisions over whether to pursue negotiations with the Afghan government.
"The young generation, maybe separated from the traditional Taliban leaders when they want to have conflict by war as solution."
Analysts believe the Taliban already confronts divisions within its ranks, and the factions disagree on whether to pursue the peace process.
Omar, who was the Taliban's head of state from 1996, had not been seen in public since the U.S.-led coalition toppled his government in 2001.
Haroun Mir, another political analyst, says the Islamic State has increased its presence in Afghanistan in the absence of Omar and has seized on the growing divisions to recruit Taliban factions into its own ranks.
In recent weeks, Taliban and IS militants have battled in several provinces, with the heaviest fighting occurring in Nangahar on the border with Pakistan.
"The ISIS itself becomes a warning for Taliban. For example, in eastern Nangahar, they were able to kick out Taliban from some of the districts. That is also a danger for the peace process, because I don't think that all Taliban would agree with the peace process. Some of the field commanders, they might refuse and they could become members of Daesh."
The Taliban and the Afghan government held their first formal talks in Pakistan in early July.
Pakistan, which had been set to play host to the second round of talks, says the postponement was requested by the Taliban leadership, citing the uncertainty caused by Omar's death as the reasons.
Meanwhile the Chinese Foreign Ministry also released a statement on Thursday, calling on all parties to focus on national unity and lasting peace in Afghanistan and continue to push forward the peace and reconciliation process.
For CRI, I am Sophie Williams.
