It said he died 10 days ago in an operation led by Afghan special forces in the eastern Nangarhar province.
Hasib is believed to have been behind March's attack on a military hospital in Kabul, killing more than 30 people.
Last month, the Pentagon said Hasib had probably been killed in a raid by US and Afghan special forces.
In April, the US military dropped its largest non-nuclear bomb ever used by America in a conflict on a system of tunnels believed to be used by IS militants in Nangarhar.
IS announced it was moving into Afghanistan and Pakistan when it declared its so-called Khorasan Province in 2015, and has since carried out a number of attacks.
In July 2016, a suicide bomb attack on a rally in Kabul killed about 80 people.
Three months later, two similar attacks during the religious festival of Ashura claimed about 30 lives, and in November 2016 an attack at a mosque in Kabul killed more than 30.
IS also claimed a suicide attack at Kabul's Supreme Court in February that killed 22 people, and the group has stepped up activity in both Afghanistan and Pakistan.
The head of so-called Islamic State (IS) in Afghanistan, Abdul Hasib, has been killed, President Ashraf Ghani's office has said.