The New York Times, citing a US official, reported US strikes on Iran were under way. A source told Reuters that Iran's supreme leader, Ayatollah Ali Khamenei, was not in Tehran and had been transferred to a secure location.
The attack, coming after Israel and Iran engaged in a 12-day air war in June, follows repeated US-Israeli warnings that they would strike again if Iran pressed ahead with its nuclear and ballistic missile programs.
"The State of Israel launched a pre-emptive attack against Iran to remove threats to the State of Israel," Defence Minister Israel Katz said.
An Israeli defence official said the operation had been planned for months in co-ordination with Washington, and the launch date was decided weeks ago.
Explosions were heard in Tehran on Saturday, Iranian media reported, and sirens sounded across Israel around 8.15am local time in what the military said was a proactive alert to prepare the public for the possibility of an incoming missile strike.
The Israeli military announced the closure of schools and workplaces, with exceptions for essential sectors, and a ban on public airspace.
Israel closed its airspace to civilian flights, and the airports authority asked the public not to go to any of the country's airports.
The US and Iran renewed negotiations in February in a bid to resolve the decades-long dispute through diplomacy and avert the threat of a military confrontation that could destabilise the region.
Israel, however, insisted any US deal with Iran must include the dismantling of Tehran's nuclear infrastructure, not just stopping the enrichment process, and lobbied Washington to include restrictions on Iran's missile program in the talks.
Iran said it was prepared to discuss curbs on its nuclear program in exchange for lifting sanctions but ruled out linking the issue to missiles.
Tehran also said it would defend itself against any attack.
It warned neighbouring countries hosting US troops it would retaliate against American bases if Washington struck Iran.
In June, the US joined an Israeli military campaign against Iranian nuclear installations, in the most direct American military action ever against the Islamic Republic.
Tehran retaliated then by launching missiles toward the US Al Udeid air base in Qatar, the largest in the Middle East.
Western powers have warned that Iran's ballistic missile project threatens regional stability and could deliver nuclear weapons if developed. Tehran denies seeking atomic bombs.