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.
Prime Minister David Cameron said he was delighted the UK would remain together and that commitments on extra powers would be honoured "in full".
Mr Cameron said the three main unionist parties at Westminster would now follow through with their pledge of more powers for the Scottish Parliament.
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.
In other developments:
- US President Barack Obama welcomed Scots' decision to stay in the UK. "Through debate, discussion, and passionate yet peaceful deliberations, they reminded the world of Scotland's enormous contributions to the UK and the world," he said.
- Police Scotland said Thursday's vote "passed off smoothly" with just six arrests across the country mainly for alleged breaches of the peace and assaults.
- Share prices rose as Scotland voted against independence.
- Polling officials said they were investigating 10 cases of suspected electoral fraud at polling stations in Glasgow.
- Royal Bank of Scotland said it would keep its headquarters in Scotland following the "No" vote.
- Wales's First Minister Carwyn Jones has called for more funding for his country after Scotland voted to stay in the Union.
- Northern Ireland First Minister Peter Robinson said a vote on the future of Northern Ireland's border was not necessary following Scotland's 'No' vote.
- Scotland rejected independence by 55% to 45%. For latest results and full coverage, go to bbc.co.uk/scotland-decides.
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 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.
Out of media player. Press enter to return or tab to continueThe moment the No side won an unassailable lead over the Yes camp
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 the 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," he added.