Mullah Akhtar Mansour, Mullah Omar’s deputy, will replace him, sources close to the Taliban leadership said.
Correspondents say the move is likely to divide the militants, and that many senior figures opposed the appointment.
Pakistan says peace talks it was due to hold between the Afghan government and the Taliban have been postponed.
The Taliban had earlier distanced themselves from the talks, which correspondents said was a further sign of division within the group.
It is thought some in the Taliban would have preferred Omar’s son to succeed him, and accuse circles within the movement close to Pakistan of imposing Mullah Mansour on them.
There has been no confirmation yet from Pakistan on Omar’s death.
The Taliban leader died two years ago in a Karachi hospital according to Afghanistan, but Pakistan has always denied that he was in the country.