"The Syrian army has taken full control of the town of Marj al-Sultan and its airport in Eastern Ghouta," a rebel bastion east of the capital, the military source said.
Rebel groups seized the airport, about 15 kilometres (nine miles) east of Damascus, in November 2012.
According to the Britain-based Syrian Observatory for Human Rights, the government forces were backed by fighters from the Lebanese Shiite militia Hezbollah.
They fully secured the airport today afternoon but "are still working to secure the town," where some rebels remain, said Observatory head Rami Abdel Rahman.
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Today's advance "will be a step towards tightening the siege around Eastern Ghouta... And reinforcing the Damascus international airport and the road that leads to it," Abdel Rahman said.
Government forces have imposed a devastating siege on the Eastern Ghouta region, which is largely held by rebels opposed to Syrian President Bashar al-Assad.
The Syrian army regularly bombards towns there, and opposition fighters shoot rockets and mortar shells west into the capital.
Yesterday, at least 45 civilians were killed in four Eastern Ghouta towns in air strikes and rocket fire by pro-regime forces, the Observatory said.
Syria's government has launched a series of simultaneous ground offensives across the country with backing by pro-regime militias and Russian warplanes.
The conflict in Syria began with anti-government demonstrations in March 2011 but evolved into a multi-front civil war that has killed more than 250,000 people and forced millions out of their homes.