Israeli intelligence Minister Israel Katz tweeted: "The (2007) operation and its success made clear that Israel will never allow nuclear weaponry to be in the hands of those who threaten its existence - Syria then, and Iran today".
The admission comes as Israel intensifies its warnings over Iran's entrenchment in neighbouring Syria and as Netanyahu steps up calls for the 2015 nuclear deal signed between its arch-foe and world powers to "fixed or nixed".
The move to go public with the strike, which has already been widely reported and cited to USA officials, comes amid repeated warnings by the Israeli prime minister, Benjamin Netanyahu, for the United States and others to take more robust action on Syria's ally, Iran.
However, Barak claims he delayed the operation so that the Israel Air Force could mount the best possible orchestrated attack.
Syria, which has joined the nuclear Non-Proliferation Treaty, has denied this.
Israeli officials said the site was almost exactly the same as a North Korean nuclear site.
Earlier Wednesday, Defense Minister Avigdor Liberman said the raid should serve as a message for "everyone in the Middle East". "Israel's policy was and has remained consistent - preventing our enemies from obtaining nuclear weapons". Eight combat jets (four F-15s and four F-16s) flew in low to avoid Syrian radar and dropped 17 tons of explosives on the reactor, which was completely destroyed. Tel Aviv has rejected global calls to join the NPT and does not allow worldwide inspectors to observe its controversial nuclear program.
Messi scores 25th in La Liga as Barca win
A swift move was finished off when Jordi Alba cut back from the left for Alcacer to slot home calmly into the bottom-right corner. Barcelona are now leading the log with 11 points ahead of second-placed Atletico Madrid who play later on Sunday.
"The government of Israel, the [Israel Defense Forces] and the Mossad [Israeli intelligence agency] prevented Syria from developing a nuclear capability", he said.
Israel and Syria have always been bitter enemies.
Israel's military sought to justify the strike on Wednesday further, noting that the Islamic State group captured the area around the facility during Syria's civil war.
Concerns over Iran's nuclear and military ambitions have long dominated Netanyahu's rhetoric on the global stage.
In 2008, the USA presented what it described as intelligence showing that the hermit kingdom had helped Syria with "covert nuclear activities".
Israel is not alone in its concern over Iran's nuclear ambitions.
Israeli Ambassador to the United Nations Danny Danon said on Wednesday that Israel will do whatever is necessary to protect itself from regional threats and beyond just hours after it was revealed that Israel destroyed a Syrian nuclear reactor back in 2007.