It is the first time that the Taliban has officially acknowledged the death of Mehsud, who heads Tehrik-e-Taliban Pakistan (TTP), a loose movement of more than a dozen armed groups.
Rehman, who is a cousin of Mehsud, said Hakimullah has been chosen by a Taliban shura (advisory council) as the new emir (head) of TTP, while denying reports of differences between the two.
Hakimullah said Rehman had been appointed as the Taliban commander in the territory controlled by Mehsud tribes in South Waziristan.
Hakimullah is considered a close aide of Mehsud, and a powerful commander who operates from the Orakzai tribal district, where US drones have conducted several missile strikes.
Recently the media repored deadly infighting among the Taliban over the succession issue as well as vast financial assets controlled by Mehsud.