Militants’ websites and Gaza media said that Mahmud al-Salfiti had escaped prison and fled the Gaza Strip in June to join the radical group in Iraq where he "died a martyr" fighting with IS.
In April 2011, Vittorio Arrigoni, a 36-year-old member of the pro-Palestinian International Solidarity Movement, was found hanged in an abandoned house north of Gaza City.
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A Salafist group had posted a video of him online and threatened to kill him unless the Hamas movement, which rules Gaza, released an unspecified number of their members.
His murder sparked outrage around the world and also among Palestinians.
Salfiti was later arrested by Hamas, and in 2012 he was sentenced to life in prison by a military court.
The sentence was later reduced to 15 years and he was incarcerated in a Hamas prison.
"Mahmud al-Salfiti, who took part in the death of the heathen Italian Arrigoni and later jailed by Hamas... managed to escape five months ago and emigrate to Islamic State to die a martyr in the battle for Anbar," a statement on jihadist websites said.
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Media in Gaza carried a similar statement and also published a picture of Salfiti.
There were no further details.
Iraqi security forces are battling to regain ground from IS militants in Anbar province west of Baghdad.
The extremist group has declared a "caliphate" on the territory it controls in Iraq and Syria.
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