Mullah Fazlullah is a particularly hardline commander whose men shot the schoolgirl activist Malala Yousafzai.
Hakimullah Mehsud was killed when missiles struck his vehicle in the North Waziristan region on 1 November.
Pakistan’s government accused the US of destroying its attempts to start peace talks with the Taliban.
Interior Minister Chaudry Nisar Ali Khan said that the drone strike was “not just the killing of one person, it’s the death of all peace efforts”.
The announcement of the new leader was made by the Taliban’s caretaker leader Asmatullah Shaheen at a news conference at an undisclosed location.
When the news was announced, there was reportedly heavy celebratory gunfire in the area around Miranshah, the main town in the tribal area of North Waziristan.
Mullah Fazlullah led a brutal campaign in Swat between 2008 and 2009, enforcing hardline Islamic law that included burning schools, and public floggings and beheadings.
A military operation was launched to retake the area.
Mullah Fazlullah fled over the border into Afghanistan but Islamabad says he has continued to orchestrate attacks in Pakistan.
He was accused of being behind a roadside bomb in September that killed Major General Sanaullah Niazi, the top commander in Swat, along with two other military personnel.
Mullah Fazlullah was known for his radio broadcasts calling for strict Islamic laws and earning him the nickname “Mullah Radio”.
The shooting of Malala Yousafzai in October 2012 sparked outrage in Pakistan and across the globe.
The teenager had spoken out against the Taliban’s restrictions on girls’ education.
The Pakistani government said a delegation had been due to fly to North Waziristan to discuss peace talks with Hakimullah Mehsud but he was killed in the drone strike the day before.
There had been some hope the new leader of the Taliban would be more open to the peace initiative.
Regional Taliban commander Khan Said Sajna, said to favor such a move, had been touted as a favorite before the latest announcement.
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