Khaled al-Asaad had been held for about a month by the group, which seized the Unesco World Heritage site in May.
The 81-year-old's family informed Syria's director of antiquities Maamoun Abdul Karim that he had been beheaded.
He described Mr Asaad as "one of the most important pioneers in Syrian archaeology in the 20th Century".
IS has demolished several ancient sites in Iraq, and there are fears that it will destroy Palmyra, one of the archaeological jewels of the Middle East.
'Insisted on staying'
The Syrian state news agency, Sana, and the UK-based Syrian Observatory for Human Rights reported that Mr Asaad had been beheaded on Tuesday at a square outside the museum in the modern town next to the ruins, also known as Tadmur.
is body was then hung from one of the Graeco-Roman columns, Mr Abdul Karim said.
IS militants had tried to extract information from him about where some of Palmyra's treasures had been hidden to save them from destruction, Mr Abdul Karim added.
Ms Asaad spent most of his life working to promote and protect Palmyra.
He was in charge of the site for four decades until 2003, when he retired. He then worked as an expert with the antiquities and museums department.
"Just imagine that such a scholar who gave such memorable services to the place and to history would be beheaded," Mr Abdul Karim told Reuters news agency.
"The continued presence of these criminals in this city is a curse and bad omen on [Palmyra] and every column and every archaeological piece in it."
Abdalrazzaq Moaz, co-director of cultural heritage initiatives at the American Schools of Oriental Research (ASOR), told the BBC that Mr Asaad had devoted his entire life to the site and died trying to protect it.
"It was hard for him to see his city under the control of these people, so he insisted on staying there," he said. "I'm sure that he was trying to convince them to not really do damage to the antiquities and the site. So for that he was killed."
Mr Moaz, a former deputy minister in charge of cultural heritage, said an archaeologist who was working on the conservation of the citadel of Damascus was also killed last week.
Since overrunning Palmyra, IS has destroyed a 2nd-Century statue of a lion and two nearby Islamic shrines, which it described as "manifestations of polytheism".
The group also released a video in July showing some 20 captured government soldiers being shot dead at Palmyra's theatre.
Syrian government forces have sought to drive IS out of the Palmyra area in recent months and there has been fierce fighting in nearby towns.
In a separate development on Tuesday, a suicide bomb attack on Kurdish security forces in the north-eastern city of Qamishli reportedly killed at least 10 people.
The United Nations also said typhoid had broken out in the besieged Yarmouk refugee camp in the suburbs of Damascus. A UN spokesman said at least six cases of the disease had been confirmed.