Sajna was chosen to lead the banned Tehrik-e-Taliban Pakistan during a meeting of its Shura or council in the tribal belt, news channels reported.
Most members of the Shura attended the meeting held at an undisclosed location. All 43 members of the council present at the gathering voted for Sajna, militant sources were quoted as saying by Dawn News.
However, some media reports said several factions of the TTP had opposed the appointment of Sajna and called for further discussions on the issue.
Enraged by the killing of Mehsud, the Taliban vowed to take "unprecedented" revenge for the drone attack in which the militant group alleged the Pakistani government was involved.
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"Our revenge will be unprecedented," Abu Omar, a Taliban commander in North Waziristan, was quoted as saying by The New York Times. Omar said he considered the Pakistani government was "fully complicit" in the drone strike.
Security was beefed up across Pakistan in the wake of Mehsud's killing. "All precautions have been taken," Interior Ministry spokesman Omar Hameed Khan told PTI.
New TTP chief Sajna, 36, is believed to have been involved in an attack on a naval base in Karachi and was credited with masterminding a 2012 jailbreak in which the Taliban freed nearly 400 prisoners in northwestern Bannu city.
"Sajna has no basic education, conventional or religious, but he is battle-hardened and has experience of fighting in Afghanistan," an official said. Sajna used to head the Taliban in South Waziristan.
He was chosen after the Shura considered three other commanders -- Umar Khalid Khurasani, Mullah Fazlullah and Ghalib Mehsud.