World financial markets plunged as nearly complete results showed a 51.8/48.2 percent split for leaving. The vote instantly creates the biggest global financial shock since the 2008 economic crisis, this time with interest rates around the world already at or near zero, stripping policymakers of the means to fight it.
The pound suffered its biggest one-day fall in history, plunging more than 10 percent against the dollar to hit levels last seen in 1985.
The vote will initiate at least two years of messy divorce proceedings with the EU and cast doubt on London's future as a global financial capital. The future of Prime Minister David Cameron -- who gambled the fate of the nation on an outcome he predicted would be catastrophic -- was doubtful at best.
An aide working in Cameron's office told reporters: "We're in uncharted territory ... Everyone's just really tired. They haven't slept."
The euro slumped more than 3 percent against the dollar on concerns a Brexit vote will do wider economic and political damage to the world's biggest trade bloc, stripped of its second largest economy.
Investors poured into safe-haven assets including gold, and the yen surged. European shares were on course to open 6 to 7.5 percent lower.
There was no immediate comment from the Bank of England. Global policymakers prepared for action to stabilize markets, with Japanese Finance Minister Taro Aso promising to "respond as needed" in the currency market.
Yet there was euphoria among Britain's eurosceptic forces, claiming a victory they styled as a protest against British political leaders, big business and foreign leaders including Barack Obama who had urged Britain to stay in the bloc.
"Dare to dream that the dawn is breaking on an independent United Kingdom," said Nigel Farage, leader of the eurosceptic UK Independence Party, calling the EU a "doomed project".
"This will be a victory for real people, a victory for ordinary people, a victory for decent people ... Let June 23 go down in our history as our independence day."
By 5.41 a.m. (0441 GMT), 93 percent of the vote had been counted, making Leave's lead impossible to reverse.
Asked if Cameron, who called the referendum in 2013 and campaigned to stay in the bloc, should resign if Britain voted for Brexit, Farage said: "Immediately."
The United Kingdom itself now faces a threat to its survival, as Scotland voted 62 percent in favor of staying in the EU and is likely to press for a new referendum on whether to become independent after its 2014 vote to stay in the UK.
Scottish First Minister Nicola Sturgeon said Thursday's vote "makes clear that the people of Scotland see their future as part of the European Union."
Northern Ireland's largest Irish nationalist party, Sinn Fein, said the result intensified the case for a vote on whether to quit the United Kingdom.
European politicians reacted with shock. "Please tell me I'm still sleeping and this is all just a bad nightmare!" former Finnish Prime Minister Alexander Stubb tweeted.
The decision will embolden populists across the continent to press for their own renegotiations and referendums. Dutch anti-immigration leader Geert Wilders called for a referendum on the Netherlands' EU membership: “We want be in charge of our own country, our own money, our own borders, and our own immigration policy."
Quitting the EU could cost Britain access to the EU's trade barrier-free single market and mean it must seek new trade accords with countries around the world. President Barack Obama says it would be at the "back of a queue" for a U.S. pact.
The EU for its part will emerge economically and politically weakened, facing the departure not only of its most free-market proponent but also a member country that wields a U.N. Security Council veto and runs a powerful army. In one go, the bloc will lose around a sixth of its total economic output.
Cameron is expected to formally report the result to his European counterparts within days and prepare negotiations for the first exit by a member state from the EU.
The British leader called the referendum in 2013 in a bid to head off pressure from local eurosceptics, including within his own party. Initially billed as an easy ride, the vote will now be his likely political epitaph. Party ally Boris Johnson, the former London mayor who became the most recognizable face of the "leave" camp, is now widely tipped to seek his job.
In the end though, the pro-EU camp was powerless to stop a tide of anti-establishment feeling and disenchantment with a Europe that many Britons see as remote, bureaucratic and mired in permanent crises.
Britain, which joined the then European Economic Community (EEC) in 1973, has always been an ambivalent member. A firm supporter of free trade, tearing down internal economic barriers and expanding the EU to take in ex-communist eastern states, it opted out of joining the euro single currency or the Schengen border-free zone.
Cameron’s ruling Conservatives in particular have risked being torn apart by euroscepticism for generations.
World leaders including Obama, Chinese President Xi Jinping, German Chancellor Angela Merkel, NATO and Commonwealth governments had all urged a "Remain" vote, saying Britain would be stronger and more influential in the EU than outside.
The four-month campaign was among the divisive ever waged in Britain, with accusations of lying and scare-mongering on both sides and rows on immigration which critics said at times unleashed overt racism.