The reclusive leader died two to three years ago, Afghan government and intelligence sources said. No further details were released.
A Taliban spokesman contacted by the BBC said the group would issue a statement shortly.
There have been several reports of Mullah Omar's death in the past. However, this is the first to be confirmed by top sources in the Afghan government.
Mullah Omar led the Taliban to victory over rival Afghan militias in the civil war that followed the withdrawal of Soviet troops.
His alliance with al-Qaeda leader Osama Bin Laden prompted the US-led invasion of Afghanistan in 2001, in the aftermath of the 9/11 attacks on New York and Washington.
Mullah Omar has since been in hiding, with a $10m US state department bounty on his head.
Over the years, the Taliban have released several messages purported to be from the fugitive leader.
The latest of these statements, from mid-July, expressed support for peace talks between the Taliban and the Afghan government.
However, the message was in the form of a text published on a Taliban website, rather than an audio or video recording - fuelling rumors that the leader was dead or incapacitated.