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The Scottish electorate's rejection of independence was greeted with delight by Prime Minister David Cameron, who said that the victory margin of around 55%-45% had settled the issue "for a generation... perhaps for a lifetime".
Speaking outside Downing Street, Mr Cameron said he would ensure that commitments to further devolution to Scotland made during the campaign would be "honoured in full".
Earlier, Scottish National Party First Minister Alex Salmond acknowledged that his dream of leading his nation to independence was over, telling supporters in Edinburgh: "Scotland has by a majority decided not at this stage to become an independent country.
"I accept that verdict of the people and I call on all of Scotland to follow suit in accepting the democratic verdict of the people of Scotland."
Turnout in the referendum on Scottish independence hit a record high for any election held in the UK since the introduction of universal suffrage in 1918.
The participation rate of 84.5% topped the previous best of 83.9% recorded in the 1950 general election and dwarfed the tallies in recent Westminster polls, which saw 65.1% vote in 2010.
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The pound has risen sharply and companies with Scottish links led the FTSE 100 Index higher as a relief rally took hold on financial markets following the rejection of independence.
Shares in Royal Bank of Scotland surged 3% while energy provider SSE, Glasgow-based engineer Weir and Standard Life were up by around 2%.
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Sterling climbed by almost 1% overnight to as high as 1.65 against the US dollar as traders reacted to the first poll results showing support for the No campaign.
PM: We have heard the voice of Scotland - and now the millions of voices of England must not go ignored.
— UK Prime Minister (@Number10gov) September 19, 2014
Let's not dwell on the distance we've fallen short - let us dwell on the distance we have travelled
— Alex Salmond (@AlexSalmond) September 19, 2014
#indyref Been up all night watching Scotland make history. A huge turnout, a peaceful democratic process: we should be proud.
— J.K. Rowling (@jk_rowling) September 19, 2014
In a dramatic announcement, Mr Cameron also announced plans to devolve powers in other parts of the United Kingdom.
JK Rowling 'proud' after No vote
"It is time for our United Kingdom to come together and to move forward," said the PM. "A vital part of that will be a balanced settlement fair to people in Scotland and importantly to everyone in England, Wales and Northern Ireland as well."
In a clear warning to nationalists that it would be wrong to seek to revive the independence debate after a vote which engaged more than 80% of the Scottish electorate, Mr Cameron said: "There can be no debates, no re-runs. We have heard the settled will of the Scottish people."
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'Astonishing' turnout breaks UK voting records
And he added: "The people of Scotland have spoken and it is a clear result. They have kept our country of four nations together and, like millions of other people, I am delighted.
"As I said during the campaign, it would have broken my heart to see our United Kingdom come to an end and I know that sentiment is shared by people not just across our country but also around the world."
Commons Leader William Hague will draw up the details of the plans to give English, Welsh and Irish MPs more powers, to be discussed in a Cabinet committee, with the same November deadline as that for the detailed proposals for Scotland.
Ukip leader Nigel Farage told Sky News: "The English are 86% by population of this Union. They've been left out of all of this for the last 18 years. We still have a situation where Scottish MPs can vote in the House of Commons on English-only issues. I think what most English people want is a fair settlement.
"Mr Cameron this morning, as a last-minute measure yet again, has decided to put William Hague in charge of a committee to try to cobble together a solution."
Shadow minister Douglas Alexander told BBC Radio 4's Today programme that Mr Cameron's announcement struck him, in some ways, as a "fairly knee-jerk reaction which ... may well have been driven more by politics than by a considered judgement of the needs of the constitution".
Voters in First Minister Alex Salmond's own constituency of Aberdeenshire resoundingly rejected independence.
With a turnout of 87.2%, there were 108,606 votes cast for No (60.3%) compared with 71,337 for Yes (39.6%).
Harry Potter author and pro-Union supporter JK Rowling was among the first celebrities to hail Scotland's decision to turn down independence.
The writer, who declared her support for the No campaign with a £1million donation earlier this year, said as the final result became clear: "Been up all night watching Scotland make history. A huge turnout, a peaceful democratic process: we should be proud."
She had previously used her website to voice her concerns about the economy and medical research in the lead-up to the referendum.
But her position on the Yes/No vote made her the subject of online abuse from pro-independence supporters over the past few months.
Scottish entrepreneur and model Michelle Mone, who had threatened to leave for England if the nation voted Yes, said both sides had fought passionately.
Hollywood star Alan Cumming urged fellow Yes voters not to give up campaigning for more powers for Scotland following the defeat.
The X-Men actor tweeted this morning: "My YES friends, let's turn our passion towards ensuring the Devo Max promises the Westminster establishment have made to us are delivered."
He later added: "Yes still means something. Please try to remember that."
There were also wins for Yes in three of Scotland's 32 local authority areas - Dundee, West Dunbartonshire and North Lanarkshire.
While there was a comfortable majority in Dundee, the turnout in the city was 78.8% - lower than many other parts of Scotland, indicating that the Yes campaign has not managed to get voters out in sufficient numbers.
The turnout in Glasgow was even lower at 75%, with 194,779 Yes votes (53.49%) and 169,347 No votes (46.51%).
SNP leader Mr Salmond had been expected to make an appearance at the Aberdeen Exhibition and Conference Centre (AECC) but instead went directly to Edinburgh from his home in Strichen.
Sir Malcolm Bruce, Liberal Democrat MP for Gordon, said: ''The point about this area is that it's Alex Salmond's backyard and his basic proposition has been overwhelmingly rejected here in Aberdeenshire, which I think will have implications.''
On the First Minister's decision not to appear at the AECC count, Sir Malcolm said: ''He only likes to come for acclamation, he doesn't like to come and commiserate with his troops. I think good leaders should be with their troops whether they win or lose but he only wants to be the centre of attention.
''He was coming here until he got first indication that it wasn't going well and he immediately aborted it.''