The terrorist Nusra Front group also published a photograph showing the bodies of five men, their hands tied and their mouths bound with handkerchiefs.
Bloodstains can be seen on the ground next to the bodies, AFP reported.
The two soldiers among the group that was executed in the Eastern Ghouta area east of Damascus included a member of Syria's elite Republican Guard, the statement said.
It is the latest in a growing series of accounts of rebel savagery in the country.
Syria has been gripped by deadly unrest since 2011. According to reports, the Western powers and their regional allies -- especially Qatar, Saudi Arabia, and Turkey -- are supporting the militants operating inside Syria.
Syria crisis started as pro-reform protests but with interventions by the United States, UK and their regional and western allies it soon turned to a massive insurgency which took in numerous terrorist groups from all over Europe and the Middle East to wage one of the bloodiest wars the region in the recent history.
According to the United Nations, over 100,000 people have been killed and millions displaced in the violence.
BA/BA