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 solution to the West Lothian question – the fact that Scottish MPs can vote on English issues at Westminster, and not the other way round.
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 (nearly 85%) 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.
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.
He also claimed th campaign had put “a scare and a fear of enormous proportions” at the heart of the Westminster establishment.
“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,” he added.
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.
BBC political editor Nick Robinson said that although the result was decisive, the constitutional implications were far from settled.
He said: “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.”
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.”
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.
'Cry for change'
“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.”
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.”