For two years, Syrian soldiers stationed at the airbase have been under an ISIL siege.
"The army managed to break through to Kweiris defenders, lifting the siege which had lasted over two years," the military source said.
The source added that "this became possible after the liberation of Sheikh Ahmad [a village 2 km away from the airbase]."
Syrian government forces continue their offensive in the Aleppo province in the north of the country.
Over the weekend, the Syrian army supported by popular forces advanced in the area, leaving dozens of the militants dead or wounded.
In October 2015, the Syrian army, with support of Russian aircraft deployed in Syria at the request of Syrian President Bashar Assad, started a military operation, trying to free territories controlled by the Islamic State and the Nusra Front militants.