Syria's director of antiquities said that the family of Khaled Asaad had informed him that the 82-year-old scholar was executed by the extremist group on Tuesday.
Islamic State militants have executed an antiquities expert in the ancient Syrian city of Palmyra.
Khaled Assad was taken hostage by the group shortly after they captured the UNESCO World Heritage city in May.
Syria’s director of antiquities Maamoun Abdulkarim said Mr Assad’s family had informed him that the 82-year-old scholar had been publicly executed and his body hung in the main square on Tuesday.
Assad had been working in Palmyra for 50 years and was head of antiquities at the Roman-era ruins, considered one of the most important historical sites in the Middle East.
ISIL militants have previously destroyed precious artefacts in Iraq and Syria but it is unknown whether they have damaged sites in Palmyra.