Prime Minister David Cameron is to step down by October after the UK voted to leave the European Union.
In a statement outside Downing Street, he said he would attempt to "steady the ship" over the coming weeks and months but that "fresh leadership" was needed.
The PM had urged the country to vote Remain but 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".
The pound fell to its lowest level against the dollar since 1985 as the markets reacted to the results.
Flanked by wife Samantha, Mr Cameron said 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.
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."