Syrian government forces launched an offensive on these areas on April 20 seeking to put an end to the presence of terrorist groups in southern Damascus and unblock the strategic Damascus-Amman highway.
The military source quoted by SANA said a ceasefire that began on Sunday and would remain in place until noon (0900 GMT) on Monday had allowed for the evacuation of women and children from the area.
Their retreat, confirmed by the Syrian Observatory for Human Rights, a monitoring group, ended weeks of fighting that had reduced the camp, once home to about 160,000, to smoking, dusty rubble.
Meanwhile, Islamic State militants have completed evacuation of fighters and civilians from Yarmuk.
Damascus is completely freed from militants as the Syrian Army clears the last stronghold, according to the source. The area south of Damascus was the scene of intense airstrikes by the Syrian government to capture the area.
It follows months of battles between ISIS fighters and Syrian government and allied troops in southern Damascus, leaving scores dead and leaving the already battered Yarmouk refugee camp an even greater scene of destruction.More news: Brussels calls on Italy to stay committed to the 'European path'
The Observatory said some IS fighters were permitted to leave Yarmouk and the adjacent al-Tadamon neighbourhood the previous night. In his first major foreign policy speech since taking the post as the top USA diplomat, he issued a list of demands that he said should be included in any new nuclear treaty with Iran, including that it "withdraw all forces" from Syria, halt support for Hezbollah and stop threatening Israel.
Takfiri terrorists have lost much of the territory they once held in Syria amid sweeping gains by government forces on the ground.
Syria's war erupted in 2011 with protests against Syrian regime leader Bashar al Assad, including in the capital.
Assad's troops launched their offensive on southern Damascus a month ago, taking advantage of the gains enjoyed since Russian Federation entered the war on their side in 2015.
Bahram Ghasemi told reporters on Monday that no one can force Tehran to do anything it doesn't desire to do.
Russian Federation and Iran have been Assad's strongest backers and have joined the war on his side.
The first group of ISIS fighters was transferred by bus out of southern Damascus on Sunday, the monitor said.