It's a deal. Or, to be strictly accurate, it's a framework deal, which means that Iran and the six major powers with whom it's been negotiating over its nuclear research programme still have a few i's to dot and t's to cross.
Even so, it's definitely worth celebrating. Not so long ago, there was a distinct possibility that Israel, with or without tacit US approval, might launch air strikes against Iran, with incalculable consequences for the region.
It's only three years since the then US defence secretary Leon Panetta was reliably quoted as saying they he believed there was "a strong likelihood" that Israel was about to start bombing Iran. Five years before that, a senior retired Israeli military official said: "If the Americans do not take military action against Iran, we'll do it ourselves.”
And only a matter of weeks ago, the Israeli prime minister Benjamin Netanyahu was in Washington to make a deeply controversial speech to the US Congress on the perils of doing a deal with Tehran. The Obama administration, to its credit, ignored him.
So the announcement from Lausanne on Thursday night was immensely significant. But so was the first phone call that President Obama made after the deal was done -- to King Salman of Saudi Arabia. (Mr Netanyahu, it seems, had to wait.)
Because the Saudis are every bit as worried about the prospect of a stronger Iran as the Israelis are. If this deal is good for Iran -- and if sanctions are lifted, it will be very good indeed for Iran -- then the thinking in Riyadh is likely to be that it's bad for Saudi Arabia. It's not just sectarian rivalry between Sunni Riyadh and Shia Tehran: it's also good, old-fashioned strategic rivalry in one of the most febrile regions on earth.
It may even be that the Saudis' unusually assertive military intervention against Shia rebels in Yemen was at least partly due to Riyadh's determination to send a message to Tehran: you may get a deal in Lausanne, but you won't automatically get what you want elsewhere.
So let us assume that the Iran nuclear deal does stick: how likely is it that for the first time since the 1979 revolution, relations with Washington will return to something resembling normal?
Not very, is the short answer, at least as long as Iran's leaders continue to back President Assad in Syria, Hizbollah in Lebanon and Hamas in the Palestinian territories. On the other hand, in Iraq, where Iranian fighters are in the forefront of the ground war against Islamic State while US warplanes are in action overhead, the two countries look almost like allies.
And here's something else that's worth considering: what will be the effect in Iran itself of the Lausanne deal? It will be presented, obviously, as a tremendous victory for the leadership -- but although President Rouhani has been backed by the country's supreme leader, Ayatollah Ali Khamenei, he still has plenty of hard-line opponents who will try to prevent the deal being finalised.
Rouhani owed his election victory in 2013 to a promise to get the crippling economic sanctions lifted by, in his words, "increasing mutual trust" with other countries. If he can demonstrate that his approach has paid off, he will be much strengthened politically and his critics will be weakened.
As the American security analyst Fred Kaplan wrote: "Tehran’s rulers have long justified their alliance with terrorists and their repressive domestic policies by raising alarms about the threat from demonic America."
So if that threat is receding, might Rouhani then be tempted to recalibrate Tehran's support for Hizbollah and Hamas? Or will he want to buttress Iran's proud reputation as an implacable enemy of Israel by continuing to support hostile Palestinian and Lebanese groups on its borders?
Iran has been immeasurably strengthened since the US-led invasion of Iraq in 2003 (yet another example of the Law of Unintended Consequences). It now plays a crucial role in Iraq, it has foiled the attempted overthrow of its ally in Damascus, Bashar al-Assad, and in Lebanon Hizbollah is a vital political player. Most recently, its Shia allies in Yemen have forced the president to flee.
The shape of the Middle East has changed, and is continuing to change, beyond recognition, first as a result of the wave of unrest that was briefly heralded as the Arab Spring, and now by the Iran nuclear deal. No one can predict what it will look like when stability returns.
The regional analyst Abdel Moneim Said Aly, director of Cairo’s al-Ahram Center for Political and Strategic Studies, wrote in Foreign Policy: "I am 67 years old — I lived through the 1956 and 1967 wars, the Arab-Israeli peace, the revolutions and coup d’états. Despite all that, I never had the same uncertainty that I have now about the region. Everything is possible.”