The Taliban statement said Jalaluddin Haqqani had been ill and bed-ridden for several years.
"If his excellency Haqqani Sahib has departed us physically, his ideology and methodology continue to endure," it said.
Haqqani, who founded the network in the 1970s, relinquished operational leadership of the group some years ago to his son Sirajuddin Haqqani, who is now deputy leader of the Afghan Taliban.
Even the Americans know themselves that this man has been irrelevant, bed-ridden, so regardless of whether he was dead or alive, he means little for the current process
Imtiaz Gul, security analyst
"Jalaluddin Haqqani ... has been ill for quite a long period of time ... so I don't see a lot of impact in terms of reduction in violence," Mushtaq Rahim, a political analyst based in Kabul, said.
"He has already relinquished the leadership to his son ... so [I] don't expect much happening in terms of tactics, in terms of intensity of engagement," he added.
'A headache for the Afghan government'
Afghan Defence Ministry spokesman Mohammad Radmanish said the death was not expected to mean any major change for the Haqqani Network.
"Operationally, his death will not have an impact on the group," he said, adding that Haqqani's role in recent years was ideological rather than practical.
Haqqani rose to prominence as a guerrilla leader in the US-backed campaign against Soviet forces occupying Afghanistan but later allied himself with the Taliban, fighting American troops after the Taliban were removed in 2001.
His group became known for complex, well-organised attacks on both Afghan and US military as well as civilian targets and high-profile kidnappings.
"He had been engaged in so many sophisticated attacks and employed innovative techniques in the asymmetric war, creating a headache for the Afghan government," Rahim said.
"Within the Taliban ranks, he has been seen as a hero. During 1980s he became a big headache for the Russian forces."
US and Afghan officials have said the group, based in Pakistan's North Waziristan region, and considered close to al-Qaeda, operated with the support of Pakistani intelligence services. That charge is rejected by Pakistan, which has pointed to the network's early links to the CIA.
'A symbolic leader'
With Sirajuddin Haqqani, who has a $5m US bounty on his head, in operational charge, it was not immediately clear what direct impact Jalaluddin Haqqani's death would have on the armed movement.
Zahid Hussain, an Islamabad-based security analyst, said that his death won't change the Haqqani Network's policies.
"This is more significant in terms of his role in the resistance against the Soviets, but in terms of the insurgency in Afghanistan, he did not have much role in that. He was a symbolic leader, that is without doubt, but not more than that."
With hopes for peace talks raised by last June's unprecedented ceasefire, news of the death of one of the most notorious rebel commanders comes at a sensitive time for both the Taliban and Kabul's Western-backed government.
Imtiaz Gul, another security analyst, said: "The senior Haqqani had been incapacitated for several years, so dead or alive he had no significance for the Taliban any more, at least for six or seven years".
"The reconciliation process is largely dependent on where the US wants to take it. The Taliban have made it very clear that the type of conditions that the US is imposing along with the talks, they are impractical and will take us nowhere," Gul, who is based in Islamabad, said.
"Even the Americans know themselves that this man has been irrelevant, bed-ridden, so regardless of whether he was dead or alive, he means little for the current process."