The UK's European Commissioner Lord Hill is to stand down, saying "what is done cannot be undone" after the UK voted to leave the European Union.
He said he did not believe it was right for him to carry on with his work as the commissioner in charge of financial services.
But he will stay on for a period of weeks to ensure an "orderly handover".
A close ally of Prime Minister David Cameron, Lord Hill had argued for the UK to remain in the EU.
He will be replaced by Latvian politician Valdis Dombrovskis, currently European Commissioner for the euro.
Asked whether the UK would be sending anyone to Brussels to take Lord Hill's place on the Commission, Downing Street said: "It will be for the next prime minister to decide, following discussions with European partners, what role the UK plays in the European Commission, given we remain a full member of the EU until we have left."
Lord Hill's announcement comes as EU foreign ministers urged Britain to hold speedy talks on leaving the bloc, after it voted to end its membership on Thursday.
But German Chancellor Angela Merkel said she was not in favour of pushing for a hasty withdrawal, adding there was "no need to be particularly nasty in any way" in the negotiations with Britain about its exit.
In another development, Scotland's First Minister Nicola Sturgeon said she would be seeking "immediate discussions" with Brussels to "protect Scotland's place in the EU" following the so-called Brexit vote.
Ms Sturgeon has said a new Scottish independence referendum is "highly likely".
European Commissioners are among the most powerful officials in Brussels, with the ability to propose laws across a range of policy areas, but the UK will cease to have one when it leaves the EU.
'Actions have consequences'
Conservative peer Lord Hill told the BBC: "When something as huge as the decision in the British referendum takes place, actions have consequences.
"It's not possible for me to carry on properly.
"You have to listen to the will of the British people. The right thing to do is to stand down and that's what today I am announcing."
In a statement, he said he was "obviously very disappointed" about the result of the referendum, adding: "I wanted it to end differently and had hoped that Britain would want to play a role in arguing for an outward-looking, flexible, competitive, free trade Europe. But the British people took a different decision, and that is the way that democracy works."
He said he did not believe it was right for him to continue as commissioner "as though nothing had happened", but that there needed to be "an orderly handover" in the weeks ahead.
European Commission President Jean Claude Juncker said he had accepted Lord Hill's resignation "with great regret," hailing him as a "true European".
He said he had put the Conservative peer in charge of financial services "as a sign of my confidence in the United Kingdom's membership of the European Union" - but "to my great regret, this situation is now changing".
By James Landale, diplomatic correspondent
There is lots to discuss with our EU colleagues: what to do with half-used EU budgets and EU citizens living in the UK and British citizens living in the EU. There is also, of course, the thorny issue of Britain's future trading relationship with the EU once we leave.
So you might imagine everyone will want to crack on as quickly as possible.
And certainly that is the view of many EU leaders. They want to end the uncertainty for the markets and begin formal talks.
The only problem is that David Cameron wants to delay the start of exit talks until a new Conservative leader has been elected in October.
Earlier, German Foreign Minister Frank-Walter Steinmeier said negotiations on the UK's exit from the EU should begin as "soon as possible".
He made the comments after an urgent meeting of the six EU founder members to discuss the decision.
David Cameron has said he will step down by October to allow his successor to conduct talks and trigger Article 50 of the Lisbon Treaty, which will formally take the UK out of the EU after two years of exit negotiations.
Chief executive of Vote Leave, Matthew Elliott, told Reuters news agency there was no need to "swiftly invoke" Article 50, adding it was "best for the dust to settle over the summer, and during that time for there to be informal negotiations with other states".
BBC diplomatic correspondent James Landale said one expert believed the European Council - representing the 27 other member states - could trigger the negotiating process as soon as the prime minister discusses Brexit with other EU leaders.
But a European Council spokesman said triggering Article 50 was a formal act which must be "done by the British government to the European Council".
In other developments:
- Shadow foreign secretary Hilary Benn has been sacked from the shadow cabinet amid claims he was encouraging ministers to resign should Jeremy Corbyn ignore a vote of no confidence
- Credit ratings agency Moody's cut the UK's outlook to "negative"
- And the pro-Leave boss of Wetherspoons said exit anxiety was 'understandable'
Earlier, Defence Secretary Michael Fallon hit back at claims the UK government had been left rudderless following Mr Cameron's resignation statement.
He said: "The prime minister goes on, the government goes on until the autumn, until there's a new leader and a new government.
"We'll remain at our posts and we have a big agenda. We were elected only a year ago and we've set out fresh legislation which we're taking through Parliament at the moment."
'Excitement and notoriety'
A timetable for a Conservative leadership election is to be announced on Monday, with former London mayor Boris Johnson - who spearheaded the campaign to get Britain out of the EU - the favourite to get the job.
MPs will select two candidates to go forward to a vote of Conservative Party members, with the winner becoming the UK's next prime minister, as well as party leader.
Pro-EU Conservative MP Sir Alan Duncan warned that MPs must not be "railroaded" into choosing Mr Johnson.
He said party members liked the "excitement and notoriety" of Mr Johnson but electing him would be a "permanent ride on the big dipper".
Lord Hill's career
- Born in north London in July, 1960
- Read history at Cambridge University
- 1980s - Special adviser to Kenneth Clarke in Conservative cabinet
- Early 1990s - Adviser to then PM John Major during EU's Maastricht Treaty negotiations, which launched euro
- 2010 - Becomes a Life Peer as Baron Hill of Oareford and junior education minister
- Serves as leader of House of Lords and leader of Conservatives in the House