In a televised statement, the army high command said Damascus and its surroundings including villages are completely secure areas.
The Syrian army raised the country's flag over the Yarmouk Palestinian camp in Damascus on Tuesday as state media promoted what it said was the "liberation" of the last quarters of the capital from rebels and Islamic State militants.
The Britain-based Syrian Observatory for Human Rights said the month of fighting left scores of dead on both sides.
Several buses on Sunday evacuated ISIS militants from their last pockets in southern Damascus to the Syrian Desert in the east under a deal that was reached following weeks of fierce battles.
The latter was recaptured in April by pro-government forces who had laid siege to it for five years before launching a major assault.
Syrian government troops and allies controlled the al-Hajar al-Aswad district and the Palestinian Refugee Camp of Yarmouk in southern Damascus, military sources reported.
Syrian government forces and allied militias had encircled and besieged south Damascus since 2013.
A cease-fire between Syrian regime forces and Daesh militants has held for 24 hours amid reports that some of the fighters have been allowed to leave, the monitor said.
In recent months, President Bashar al-Assad has used a blend of military pressure and negotiated withdrawals to steadily flush rebels out of territory around Damascus.
"The new arrival of Daesh [IS] fighters to the Badia threatens the entire region", Said Saif, a media spokesman for the Forces of the Martyr Ahmad al-Bado Brigade, told Syria Direct.
BBC Arab affairs analyst Sebastian Usher says the price of victory in Damascus for President Assad, as nearly everywhere else in Syria, has been high - in death, destruction and displacement.
Iran and Russian Federation have joined forces in Syria, providing crucial military support to Assad's forces and giving them the upper hand in the civil war. The refugee camp, which once housed a large number of Palestinians, has been contested repeatedly since the Syrian War began. Before Syria's civil war began, it was a built-up residential area home to tens of thousands of Palestinians and Syrians. "They requested this out of fear the buses would be targeted", the resident said.
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.