The aid, which will arrive on a Russian plane to a Russian military base in northwestern Syria from France on Saturday, comes after an agreement between President Emmanuel Macron and Russian leader Vladimir Putin following talks since May.
"This operation is very significant because it shows a willingness from the Russians to work with us on a matter of priority," said the French diplomatic source. "This area is crying out for help."
A joint Franco-Russian statement confirmed the accord.
Pro-government forces retook the eastern Ghouta region from rebels in April after besieging the region for several years and launching a final brutal bombing campaign with their Russian allies.
Little aid has entered eastern Ghouta, where about 500,000 people live, since April, although United Nations Office for the Coordination of Humanitarian Affairs (OCHA) was able to deliver food and nutritional aid for some 25,000 people in early July.