Armament facilities and a military training camp are among the Iranian sites in Syria struck by Israeli jets early on Monday morning.
The IDF its strikes were in response to a rocket launch from Syria aimed at the Golan Heights.
"Yesterday, Iranian Quds forces operating in Syrian territory launched a surface-to-surface rocket from Syrian territory aimed at the northern Golan Heights," the Israeli military said in a statement.
"In response to the attack, during the night (Israeli military) fighter jets struck Iranian Quds Forces military targets in Syria in addition to Syrian aerial defence batteries."
Speaking on Monday morning at the opening of a new airport in Eilat, Prime Minister Benjamin Netanyahu said Israel would not permit "Iranian aggression".
"Yesterday evening, the air force struck a strong blow against Iranian targets in Syria after Iran fired a missile from there toward Israel," he said
"We do not allow such acts of aggression to pass by. We are acting against Iran and against the Syrian forces who are tools of Iranian aggression."
The open claim of responsibility marks a shift in Israeli policy.
The IDF has previously refused to acknowledge or deny involvement in strikes on Syrian territory.
There were competing reports over the number of casualties following Monday morning's strike.
The Syrian Observatory for Human Rights, a war monitoring service based in London, said 11 fighters had died in the strike, including at least two Syrians.
But Russian sources said the number of Syrian soldiers killed was four, and that a further six were wounded.
