With the results in from all 32 council areas, the “No” side won with 2,001,926 votes over 1,617,989 for “Yes”.
Scotland’s First Minister Alex Salmond called for unity and urged the unionist parties to deliver on more powers.
UK Prime Minister David Cameron said he was delighted the UK would remain together and said the commitments on extra powers would be honoured.
Mr Cameron said the three main unionist parties at Westminster would now follow through with their pledge of more powers for the Scottish Parliament.
“We will ensure that those commitments are honoured in full,” he said.
He announced that Lord Smith of Kelvin, who led Glasgow’s staging of the Commonwealth Games, would oversee the process to take forward the commitments, with new powers over tax, spending and welfare to be agreed by November, and draft legislation published by January.
The prime minister also acknowledged that the people of England, Wales and Northern Ireland must have a bigger say over their affairs.
And he promised a resolution to the West Lothian question – the fact that Scottish MPs can vote on English issues at Westminster.
The result became a mathematical certainty at 06:08, as the returning officer in Fife announced a comfortable No vote.
Shortly afterwards, Mr Salmond said he accepted the defeat and called for national unity.
He said the referendum and the high turnout had been a “triumph for the democratic process” and promised to keep his pledge in the Edinburgh Agreement which paved the way for the referendum to respect the result and work for the benefit of Scotland and the United Kingdom.
He told supporters: “The unionist parties made vows late in the campaign to devolve more powers to Scotland.
“Scotland will expect these to be honoured in rapid course – as a reminder, we have been promised a second reading of a Scotland Bill by March 27 next year.
And the First Minister said: “Whatever else we can say about this referendum campaign, we have touched sections of the community who have never before been touched by politics, these sections of the community have touched us and touched the political process.”
In a rallying call to his supporters, Mr Salmond urged the Yes voters to reflect on how far they had come.
“I don’t think any of us, whenever we entered politics, would have thought such a thing to be either credible or possible,” he said.
“Over the last few weeks we have seen a scare and a fear of enormous proportions – not a scaremongering directed at the Scottish people but the scare and the fear at the heart of the Westminster establishment as they realise the mass movement of people that was going forward in Scotland.
“Today of all days as we bring Scotland together, let us not dwell on the distance we have fallen short, let us dwell on the distance we have travelled and have confidence the movement is abroad in Scotland that will take this nation forward and we shall go forward as one nation.”
This margin of victory for the Better Together campaign – 55% to 45% – was greater by about 3% than that anticipated by the final opinion polls. The winning total needed was 1,852,828.
Speaking in Downing Street, Mr Cameron said the result was decisive.
He said: “Now the debate has been settled for a generation, or as Alex Salmond has said: ‘Perhaps for a lifetime’.
“So there can be no disputes, no re-runs; we have heard the will of the Scottish people.”
The prime minister also spoke of the implications for the other nations of the UK.
“In Wales there are proposals to give the Welsh Government and Assembly more powers and I want Wales to be at the heart of the debate on how to make the United Kingdom work for all our nations,” he said.
“In Northern Ireland, we must work to ensure that the devolved institutions function effectively.”
Mr Cameron said “millions of voices of England must also be heard”.
“The question of English votes for English laws, the so-called West Lothian question, requires a decisive answer so just as Scotland will vote separately in the Scottish Parliament on their issues on tax, spending and welfare, so too England as well as Wales and Northern Ireland should be able to vote on these issues.
“And all this must take place in tandem with and at the same pace as the settlement for Scotland.”
The people have spoken. But it’s not over.
BBC political editor Nick Robinson
The people have spoken. Scotland has rejected independence. The result has been accepted by both sides. So that you might think is that. Not a bit of it.
The fact that over 1.5m British citizens voted to break away from the rest of the UK, the fact that a majority in Scotland’s biggest city – Glasgow – backed independence, the fact that the Westminster establishment briefly thought this vote was lost, is the reason for that.
The leaders of the three UK parties are now promising significant constitutional change and not just for Scotland but for England, Wales and Northern Ireland as well.
They have agreed on a timetable for giving more powers to the Scottish Parliament but are a long, long way from agreeing proposals.
Alistair Darling, who led the Better Together campaign, said the people of Scotland had “chosen unity over division and positive change rather than needless separation”.
“It is a momentous result for Scotland and also for the United Kingdom as a whole,” he said.
Mr Darling said the result had “reaffirmed all that we have in common and the bonds that tie us together”, adding: “Let them never be broken.”
“As we celebrate, let us also listen,” he said.
“More than 85% of the Scottish population has voted. People who were disengaged from politics have turned out in large numbers.
“While they have voted on the constitution, that was not the only or perhaps the major issue that drove them to the polls.
“Every political party must listen to their cry for change, which could be echoed in every part of our United Kingdom but had this opportunity to express itself in Scotland.”
Constitutional revolution on the way
Analysis by Andrew Marr
What started as a vote on whether Scotland would leave the UK has ended with an extraordinary constitutional revolution announced outside Downing Street by the Prime Minister.
It throws down the gauntlet to the Labour Party, and hints that we are going to see very big change coming and it had better come quickly.
We always used to be told that if you laid all the economists in the world end to end they still wouldn’t reach a conclusion and I think that could be said often about parliamentary committees and inquiries and commissions.
Well, it can’t happen this time because it’s not taking place in a sealed room with the Westminster parties, the old smug consensus, getting round an argument with each other as before.
This is really taking place in a huge glass house, being watched by all the Scottish voters and by millions of people around the UK.
What the Scottish shock has done is produce a constitutional revolution on a very, very tight timetable. Possibly the most exciting political story in my lifetime.
Mr Darling thanked his “great team of volunteers” who had worked on the Better Together campaign.
He added: “You represent the majority of opinion. Your voices have been heard. We have taken on the argument and won. The silent have spoken.”
Mr Salmond’s deputy, Nicola Sturgeon, said in an earlier concession statement that there was a “real sense of disappointment that we have fallen narrowly short of securing a ‘Yes’ vote”.
But she said the country had been “changed forever” and vowed to work with “anyone in any way” to secure more powers for Scotland.
The vote was the culmination of a two-year campaign. Talks will now begin on devolving more powers to Scotland.
Glasgow, Scotland’s largest council area and the third largest city in Britain, voted in favour of independence by 194,779 to 169,347, with Dundee, West Dunbartonshire and North Lanarkshire also voting “Yes”.
But Edinburgh, the nation’s capital, rejected independence by 194,638 to 123,927, while Aberdeen City voted “No” by a margin of more than 20,000 votes.