The next move is London’s. It falls to the British government to decide when to activate Article 50 of the Lisbon treaty, which will set the exit process in motion.
But the European Union must also deliver a coherent, well-judged response worthy of the moment. The early signs have hardly been encouraging.
Speaking early on Friday morning, European Commission president Jean-Claude Juncker was asked whether this was the beginning of the end of the European Union.
It was the sort of question a canny politician turns on its head; Juncker could have taken the opportunity to deliver a defence of the European ideal, to recall the achievements and the values that have underpinned the post-war integration project and that British voters had chosen to reject.
Instead Juncker responded with a curt "No" and walked off the stage – a tone-deaf response that was followed by the surreal sound of vigorous applause from the body of the press room in Brussels.
The following day, the foreign ministers of the six founding members of the European Economic Community – France, Germany, Italy, Belgium, the Netherlands and Luxembourg – met in Berlin and issued a joint statement calling for the UK to swiftly set in motion the withdrawal process.
Whoever thought this was what the occasion demanded – a demarche from the original six, led by the old Franco-German motor, taking it upon themselves to usher London towards the door? It wasn’t merely that the optics were bad. The meeting suggested a degree of consensus that evaporated as soon as the statement had been issued.
Within hours, German chancellor Angela Merkel was calling for a calm, measured response, distancing herself from France by suggesting there was no particular need for London to rush its departure. "Quite honestly, it should not take ages, that is true, but I would not fight now for a short time frame," she said.
Behind this is a deeper disagreement between how to respond to the decision and what it means for the European project more broadly.
Brexit will bring three types of change to the EU, according to Prof Brigid Laffan, director of the Robert Schuman Centre for Advanced Studies at the European University Institute in Florence.
First, it will alter the internal power balance in the bloc. “It will leave Germany in a very lonely position,” she says.
It also has serious implications for France, which, notwithstanding its perennial disagreements with London on various economic and social policy questions, stands to lose one of its major trading partners and a close collaborator on security and defence.
Second, the outcome will affect EU policy debates on issues such as financial regulation, climate change and trade.
Third, Prof Laffan points out, it will encourage parties elsewhere on the Continent who seek the exit of their own countries from the union.
"The political forces it will embolden are the radical right, which combines both anti-migration and anti-Europeanism. A member state is leaving, and the key issue on which the campaign pivoted was not the economy but migration. It has unknown and unknowable consequences for the issue of migration across Europe, " she adds. The EU "is strong enough to find the right answers", Merkel said at the weekend. But it's not at all clear what the question is.
Many of Europe’s power brokers will look at the British Leave campaign – propelled as it was by an inchoate mix of grievances on everything from globalisation to immigration and local services, underlaid by identity politics and sprinkled with a toxic dose of lies and exaggeration – and conclude that the EU itself was largely incidental to the British debate.
And yet there’s no doubt that the result confirms a trend that has been hardening across the continent for many years: a repudiation of the principles the EU is founded upon, such as pooled sovereignty, freedom of movement and cross-border political cooperation.
Already one of the points of tension among European leaders is that age-old question the EU asks itself in times of crisis: should we respond with more or less Europe? And on this Paris and Berlin are at odds. “Europe can no longer go on as before,” French president François Hollande declared. Rather, he said, it must “focus on the essentials” of “investment for growth and jobs”, “tax and social harmonisation” and “reinforcement of the euro zone and its democratic governance”. In other words, France sees an opportunity to assert its long-cherished priorities, notably by strengthening the euro zone as an inner core of the integration project.
In this it finds allies in Juncker and the president of the European Parliament, Martin Schulz, both of whom also called for a quick start to the Brexit process. Merkel prefers to sit tight and see how this plays out. This was not the time for "quick and simple solutions and would divide Europe more", she said.
The French desire for a quick British exit is partly driven by domestic political imperatives. The far-right Front National under Marine Le Pen, who has been riding high in the polls for the past two years, greeted the British decision with jubilation.
Hollande’s government fears a political vacuum that runs into 2017 – an election year in France – will give Le Pen room to make hay. The worst thing would be to stand still, said French foreign minister Jean-Marc Ayrault. “We have to give a new sense to Europe. Otherwise populism will fill the gap.”