In the statement, the Taliban called Haqqani a figure who devoted himself to the fight against communism and the US occupation of Afghanistan.
Zabihullah Mujahed, a Taliban spokesman, told the Associated Press in a telephone interview Tuesday that Haqqani died on Monday inside Afghanistan.
The founder of the notorious Taliban-linked Haqqani, passed operational control of the network to his son Siraj many years ago, who then became the number-two ranked commander in the Taliban.
The Haqqani network was formally designated a terrorist organization by the United States in 2012.
The network, which is based in Waziristan, a tribal area of Pakistan, is linked with both the Taliban and al Qaeda. It also operates across the border in Afghanistan.