In a statement on Wednesday, the army said Israeli warplanes struck the facility in Deir al-Zour desert on September 5-6 2007.
“The operation was carried out after complex intelligence efforts by dropping 17 tons of explosives using laser-guided bombs,” it said.
The Israeli army said that the suspected reactor “was close to being completed”.
Several Israeli media outlets published recordings and photographs of the Israeli attack on the Syrian facility.
According to Haaretz daily, the reactor was discovered by chance after five years of construction by the Syrians with the help of North Korea.
There was no comment from the Syrian regime on the Israeli admission.
Previously, Syria has denied that the bombed side was a nuclear reactor.
Last month, Israeli warplanes carried out airstrikes against Syrian and Iranian military targets in war-torn Syria.