The Syrian army has restored control over all areas surrounding the capital Damascus for the first time since early in the seven-year-old war, after pushing Daesh militants out of a south Damascus pocket, the military said.
In a televised statement Syria's army high command said Al Hajar Al Aswad and Yarmouk had been cleared of militants.
The Britain-based Syrian Observatory for Human Rights earlier said buses had entered the enclave after midnight to take out fighters and their families.
The government has denied reaching a deal with IS.
Russian Federation has conducted a military campaign in Syria since September 2015, helping reverse the course of war in Syrian President Bashar Assad's favor.
Shortly before noon Monday when the truce was supposed to end in Hajar al-Aswad, government warplanes struck IS positions as Syrian troops began pounding and advancing slowly deeper into the neighborhood.
A lot of them were former members of Al Qaeda's Syrian ex-affiliate Al Nusra Front, but Daesh fighters there also included Palestinian refugees who joined when the hard-liners took over much of the camp in 2015. The Observatory said Daesh militants began burning their posts in Yarmouk and adjacent areas.
"The Syrian government does not admit to negotiating with IS and wants to make sure the convoy is not targeted by the coalition led by Washington", he said.
Iranian officials have pledged to remain in Syria despite calls by the United States, Israel, and others for it to remove its fighters.
Yarmouk was the largest Palestinian camp in Syria and was put under crippling government siege in 2012 - making it one of the longest besiegements of Syria's war.
"The last group of fighters left on trucks, not on buses".
Pro-regime forces, specifically Palestinian militias, had been fighting since April 19 to recapture Yarmuk, Tadamun, and the nearby districts of Qadam and Hajar al-Aswad from IS.
Those operations have killed more than 250 pro-government forces and 233 militants, as well as more than 60 civilians, according to the Observatory.
"The Daesh terrorist organization is living its last hours" in the Damascus area, the TV's reporter said, using an Arabic acronym to refer to IS.