Government troops "were able to liberate all the 19 hostages... and kill the terrorist kidnappers", it added.
State television broadcast images of veiled women, boys and at least one girl surrounded by men in military uniforms near a white pick-up truck in a desert landscape.
It said the images were broadcast from the desert near the ancient city of Palmyra in the centre of the country.
Nour Radwan, a journalist based in Sweida, confirmed the liberation but said the women and children were freed in a prisoner exchange deal.
"The freeing of the remaining hostages came as part of a prisoner swap deal, and today was the second stage of that deal," he told AFP.
Two women and four children were released last month in a first step of the same agreement that also saw women and children related to IS fighters freed from regime jails, he said.
The Druze community had been hoping for the return of 20 hostages, Radwan said.
"IS told the family of one of the female hostages that they had killed her but did not send any proof," he said.
"We're waiting for them to arrive in Sweida. If there are 19 of them then it means she really was killed," he said.
The jihadists executed a 19-year-old male student among the hostages in August and then a 25-year-old woman in early October.
IS said a 65-year-old woman being held by the group also died from illness. Sweida province is the heartland of the country's Druze minority, which made up roughly three percent of Syria's pre-war population -- or around 700,000 people.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)