Mullah Akhtar, a close aide of Mullah Omar who served as his deputy for the past three years, was chosen as the new leader by Taliban Shura (top decision making body).
The council also elected Sirajuddin Haqqani, the chief of dreaded Haqqani network as deputy of the Taliban's leader.
Haqqani carries an American bounty of USD 10 million on his head as a leader of the Haqqani network, which is linked with Al-Qaeda. Haqqani network has been blamed for several deadly attacks against Western and Indian interests in Afghanistan including 2008 bombing of Indian mission in Kabul.
The Taliban shura council met at an undisclosed location in the border region of Pakistan and Afghanistan to decide on Mullah Omar's replacement.
Source familiar with the development told PTI that Mullah Akhtar was the de facto chief of the Taliban and was leading the group since death of Mullah Omar in April 2013.
"He was endorsed to continue the job and lead" the Taliban, a source said.
Hours after Mullah Akhtar's appointment, Taliban confirmed the death of Mullah Omar in a statement.
"The leadership of the Islamic Emirate and the family of Mullah Omar... announce that leader Mullah Omar died due to a sickness," a statement issued by the Taliban said, using the insurgent group's official name.
The statement did not say when and where he died but said "his health condition deteriorated in the last two weeks".
It added that three days of religious ceremonies would be held "to pray for the soul of Mullah Omar".
The Afghan government last night announced that elusive one-eyed Mullah Omar, who ruled Afghanistan from 1996 to 2001 with an iron fist before US-led forces overthrew his government, died in April 2013 in Pakistan.
The new Taliban chief is considered close to the Pakistani authorities and his election could further divide an already-fractured Taliban.
Mullah Akhtar was Omar's deputy, and was running the 20-member council after the Taliban chief's death. He has the support of Taliban's senior leadership.
He is said to be in favour of peace talks with the Afghan government, and reportedly has appointed Haji Din Muhammad to participate in the peace process.
He was one of the top Taliban leaders whose accounts the US had frozen as a result of the 9/11 attacks. He was also one of two senior Taliban leaders named by Mullah Omar to replace the group's then No.2 Mullah Abdul Ghani Barader, who was arrested in Pakistan in February 2010.
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