Prime 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".
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 frontrunner 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.
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."
Cameron said he is not the “captain” that will steer the country through negotiations to leave the 28-nation bloc, which he opposed, and said he would tender his resignation by the time of the Conservative party conference in the fall.
“I do not think it would be right for me to try to be the captain that steers our country to its next destination,” the British leader said outside his official Downing Street residence in London.
The UK requires “fresh leadership,” he said, adding that the will of the British people must be respected.
Cameron said that he would leave it to his successor to trigger the formal process for Britain to leave the European Union.
“I think it’s right that this new prime minister takes the decision about when to trigger Article 50,” Cameron said.
Britain has voted to leave the European Union by 51.9 percent to 48.1 percent, final results from all 382 of Britain’s local counting centers showed on Friday.
The final result showed 17.4 million people had voted “Leave” and 16.1 million people had voted “Remain” in the EU membership referendum.
World financial markets were rocked Friday by Britain’s unprecedented vote, with stock markets and oil prices crashing and the pound hitting its lowest level in three decades.