The group published an obituary for the jihadist, whose real name was Mohammed Emwazi, in its online magazine Dabiq.
In November the US military said it was "reasonably certain" it had killed him in the IS-stronghold of Raqqa.
Emwazi appeared in beheading videos of victims including UK aid worker David Haines and taxi driver Alan Henning.
Who was Mohammed Emwazi?
In the eulogy, Kuwaiti-born Emwazi is referred to as Abu Muharib al-Muhajir, his nickname in the group and the details of his death confirm the US version of events.
The jihadist group said Emwazi was killed on 12 November "as the car he was in was targeted in a strike by an unmanned drone in the city of Raqqa, destroying the car and killing him instantly".
A smiling picture of the militant, who appears unmasked looking towards the ground, accompanies the text, which is written in tribute form to a man they describe as an "honourable brother". Read more on bbc.