SANA news agency said in its report that the operation occurred in the Hamima area east of the historic town of Palmyra. It said all IS fighters in the area where the hostages were held have been killed.
The Suwayda 24 activist collective quoted local officials as saying the women and children held by IS have all been freed.
"My happiness is huge," Nashaat Abu Ammar, whose wife, two sons and daughter are among those freed, told The Associated Press by telephone.
The 19 women and children were among 30 people kidnapped by IS in the southern province of Sweida on July 25 when militants of the extremist group ambushed residents and went on a killing spree that left at least 216 people dead.
The rare attacks in Sweida province, populated mainly by Syria's minority Druze, came amid a government offensive elsewhere in the country's south. The coordinated attacks across the province, which included several suicide bombings, shattered the calm of a region that had been largely spared from the worst of the violence of Syria's seven-year long civil war.
A Syrian opposition war monitor contradicted the reports on state media, saying IS set free the hostages in return for the government's release of women related to IS fighters and commanders who were held by Syrian authorities as well as a monetary payment.
The Britain-based Syrian Observatory for Human Rights said it was not immediately clear how much money the government paid for the release of the hostages.
State TV aired footage of the women, children and teenagers in a desert area standing with soldiers who gave them bread and water. The soldier then asked the women and children for their names and wrote them on a piece of paper. The TV later aired footage showing the former hostages having meals around a table.
"We are living the joy of victory in Syria," Druze cleric Sheikh Kameel Nasr told Syrian state TV.
Since July, one woman died in IS custody while another was shot dead by the extremists. In August, a 19-year-old man was also killed in detention.
Six other hostages, two women and four children, were freed in an exchange with the government last month. Negotiations were expected to free the remaining hostages but after the talks failed, Syrian troops launched a broad offensive against IS in southern Syria.
The July 25 attack on the southern city of Sweida and nearby villages was one of the deadliest by the extremists since they lost most of the land they once held in Syria and Iraq.
"I am so happy they have been freed and I thank the Syrian army for that," Abu Ammar said. The man said he is getting ready to leave his village to the provincial capital of Sweida where the freed were expected to be brought later.
By sunset, scores of people gathered in the city of Sweida waiting for the return of the former hostages.
Elsewhere in Syria, opposition activists and paramedics reported that two blasts in rebel-held parts of northern Syria have inflicted casualties.
The Observatory said the first explosion occurred in the northern town of Azaz wounding six children while the opposition's Syrian Civil Defense said four were wounded including three children.
The observatory and other opposition activists reported another blast in the town of Jinderis saying a bomb went off outside an office of the Turkey-backed Failaq al-Sham rebel group killing three fighters and wounding seven.
Azaz and Jeideris are controlled by Turkey-backed opposition fighters. The two towns were once controlled by Kurdish fighters opposed to Turkey.
Explosions in rebel-held parts of northern Syria are not uncommon and have killed and wounded dozens in recent months.
Mroue reported from Beirut.
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