rime Minister David Cameron is to step down by October after the UK voted to leave the European Union.
Speaking outside 10 Downing Street, he said "fresh leadership" was needed.
The PM had urged the country to vote Remain but was defeated by 52% to 48% despite London, Scotland and Northern Ireland backing staying in.
UKIP leader Nigel Farage hailed it as the UK's "independence day", while Boris Johnson said the result would not mean "pulling up the drawbridge".
Scottish First Minister Nicola Sturgeon said she was "absolutely determined" to keep Scotland in the EU so a second Scottish independence referendum was now "highly likely".
German chancellor Angela Merkel expressed "great regret" at the outcome, and EU chiefs said they expected the UK to begin negotiations to leave "as soon as possible, however painful that process may be".
But Boris Johnson, the ex-London mayor and public face of Vote Leave who is now a front-runner to be next prime minister, said there was "no need for haste" about severing the UK's ties.
He said voters had "searched in their hearts" and the UK now had a "glorious opportunity" to pass its own laws, set its own taxes and control its own borders.
Another leading Leave campaigner, Labour's Gisela Stuart, said the UK would be a "good neighbour" when it left the EU.
The pound fell to its lowest level against the dollar since 1985 as the markets reacted to the results.
The slide halted when the Bank of England said it stood ready with £250bn of extra funding to ensure market stability. But the pound remains 8% down against the dollar, and 6% lower against the euro.
Flanked by his wife Samantha, Mr Cameron announced shortly after 08:15 BST that he had informed the Queen of his decision to remain in place for the short term and to then hand over to a new prime minister by the time of the Conservative conference in October.
He would attempt to "steady the ship" over the coming weeks and months, but that it would be for the new prime minister to carry out negotiations with the EU and invoke Article 50 of the Lisbon Treaty, which would give the UK two years to negotiate its withdrawal, he said.
"The British people have voted to leave the European Union and their will must be respected," said Mr Cameron. "The will of the British people is an instruction that must be delivered."
Speaking outside 10 Downing Street, he said "fresh leadership" was needed.
The PM had urged the country to vote Remain but was defeated by 52% to 48% despite London, Scotland and Northern Ireland backing staying in.
UKIP leader Nigel Farage hailed it as the UK's "independence day", while Boris Johnson said the result would not mean "pulling up the drawbridge".
Scottish First Minister Nicola Sturgeon said she was "absolutely determined" to keep Scotland in the EU so a second Scottish independence referendum was now "highly likely".
German chancellor Angela Merkel expressed "great regret" at the outcome, and EU chiefs said they expected the UK to begin negotiations to leave "as soon as possible, however painful that process may be".
But Boris Johnson, the ex-London mayor and public face of Vote Leave who is now a front-runner to be next prime minister, said there was "no need for haste" about severing the UK's ties.
He said voters had "searched in their hearts" and the UK now had a "glorious opportunity" to pass its own laws, set its own taxes and control its own borders.
Another leading Leave campaigner, Labour's Gisela Stuart, said the UK would be a "good neighbour" when it left the EU.
The pound fell to its lowest level against the dollar since 1985 as the markets reacted to the results.
The slide halted when the Bank of England said it stood ready with £250bn of extra funding to ensure market stability. But the pound remains 8% down against the dollar, and 6% lower against the euro.
Flanked by his wife Samantha, Mr Cameron announced shortly after 08:15 BST that he had informed the Queen of his decision to remain in place for the short term and to then hand over to a new prime minister by the time of the Conservative conference in October.
He would attempt to "steady the ship" over the coming weeks and months, but that it would be for the new prime minister to carry out negotiations with the EU and invoke Article 50 of the Lisbon Treaty, which would give the UK two years to negotiate its withdrawal, he said.
"The British people have voted to leave the European Union and their will must be respected," said Mr Cameron. "The will of the British people is an instruction that must be delivered."
