The decision was taken at a meeting of the Tehrik-e- Taliban Pakistan's Shura (Council), media reports said.
Most of the members of the council were present in the meeting held at an undisclosed location though all could not attend it.
All 43 members of the Shura attending the meeting voted in favour of Sajna, militants sources were quoted as saying by Dawn News. It said the election was not confirmed by factions of the militant grouping.
"Sajna has no basic education, conventional or religious, but he is battle-hardened and has experience of fighting in Afghanistan," an official had said earlier.
More From This Section
Sajna was heading the South Waziristan Taliban.
The council considered four names for the top post, including Sajna, Umar Khalid Khurasani, Mullah Fazlullah and Ghalib Mehsud.
Mohmand Taliban chief Umar Khalid Khurasani was a strong contender as he was the only surviving senior commander who had directly led operations under Hakimullah.
Hakimullah, in his mid 30s, and five other Taliban militants were killed and two others wounded yesterday when a US drone targeted a compound as he left a meeting in Danday Darpakhel area of North Waziristan.
They were buried today at undisclosed locations in different parts of North Waziristan.
Meanwhile, enraged at the killing of its top leader, the Taliban has vowed to take "unprecedented" revenge for the attack in which the militant group alleges the Pakistani government was also involved.
"Our revenge will be unprecedented," Abu Omar, a Taliban commander in North Waziristan, was quoted as saying by the New York Times report. Omar said he considered the Pakistani government was also "fully complicit" in the drone strike.
Security has been beefed up across Pakistan in wake of Hakimullah's killing.
"All precautions have been taken," Interior Ministry Spokesperson Omar Hameed Khan told PTI.