In a statement announcing that the operation was under way, the Israeli military spokesman said Israel had the "right and duty" to respond and that its defensive and offensive capabilities were fully mobilised.
A news agency close to the Revolutionary Guards says that some military bases in the west and south west of the Iranian capital have been targeted.
The Syrian state news agency says that Israeli airstrikes have also targeted some military sites in central and southern areas of Syria.
The office of the Israeli Prime Minister Benjamin Netanyahu has released a picture of him in the operations centre of the military headquarters during the attack.