Shishani`s real name was Tarkhan Batirashvili but he was also known as Omar the Chechen.
The red-bearded jihadist was said to be a close military adviser to Islamic State leader Abu Bakr al-Baghdadi.
The confirmation came on the Amaq website, which IS regularly uses to issue news and which had denied the Pentagon`s claims in March.
It did not specify when, but the statement conflicts with the US claims made in March.
It said its strike on 4 March had taken place near the north-eastern town of Shaddadi, where Shishani had reportedly been sent to bolster local IS forces.
Last year, the US offered a $5m (£3.5m) reward for Shishani.
It said he had held numerous senior military positions within the group, including "minister of war".
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