The Haqqani network has been behind many of the co-ordinated attacks on Afghan and Nato forces in recent years.
His son is believed to have taken over control of the group in 2001.
“Just as he endured great hardships for the religion of Allah during his youth and health, he also endured long illness during his later years,” a statement from the Afghan Taliban said.
There were no details in the statement about the date or place of his death.
Rumours about Haqqani’s death have circulated for years.
In 2015, sources close to the group told the BBC that the leader had died at least a year before. This was never confirmed.
Jalaluddin Haqqani was an Afghan guerrilla leader who fought Soviet troops that occupied Afghanistan in 1980s.
US officials have admitted that at the time he was a prized asset of the Central Intelligence Agency (CIA).
However, he later allied himself to the Taliban after they took power in Afghanistan in 1996.
In its statement, the Taliban called Jalaluddin an “exemplary warrior… and among the great distinguished Jihadi personalities of this era”.
The Haqqani group have been blamed for some of the deadliest attacks in the country, including a truck bomb explosion in Kabul in 2017 that killed more than 150 people.