The sources told Reuters that the adviser, known as Sayyed Razi Mousavi, was responsible for co-ordinating the military alliance between Syria and Iran.
Iran's state television interrupted its regular news broadcast to announce that Mousavi had been killed, describing him as one of the Guards' oldest advisers in Syria.
It said he had been "among those accompanying Qassem Soleimani," the head of the Guards' elite Quds Force who was killed in a US drone attack in Iraq in 2020.
Iran's ambassador in Damascus Hossein Akbari told Iranian state TV that Mousavi was posted at the embassy as a diplomat and was killed by Israeli missiles after returning home from work.
Iranian President Ebrahim Raisi said the assassination of Mousavi showed weakness on the part of Israel.
"This act is a sign of the Zionist regime's frustration and weakness in the region for which it will certainly pay the price," Iranian media cited Raisi as saying.
The Revolutionary Guards said Israel would suffer for killing Mousavi, who held the Guards' rank of brigadier-general.
"The usurper and savage Zionist regime will pay for this crime," the Guards said in a statement read on state TV.
Foreign Ministry spokesman Nasser Kanaani told state media that: "Iran reserves the right to take necessary measures to respond to this action at the appropriate time and place."
For its part, the Palestinian Islamic Jihad group condemned the killing of Mousavi as a "cowardly act," saying he had played a vital role in supporting the resistance in the region as well as the Palestinian people and their cause.
There was no immediate comment from Israel's military.
Israel has for years carried out attacks against what it describes as Iran-linked targets in Syria, where Iranian influence has grown since it backed President Bashar al-Assad in the war that erupted in Syria in 2011.
Earlier this month, Iran said Israeli strikes had killed two Revolutionary Guards members in Syria who had served as military advisers there.
Iran has sent hundreds of Guards as "advisers" to help train and organise thousands of Shi'ite militia fighters from Iraq, Afghanistan and Pakistan to back the government in the Syrian conflict.Â
Fighters from Lebanon's Hezbollah have also worked closely with Iranian military commanders in Syria.
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