The leader of the Better Together campaign, Alistair Darling, has called the result a "momentous result for Scotland and also the United Kingdom as a whole".
He said that it "reaffirmed all that we have in common and the bonds that tie us together - let them never be broken".
But he said the surge in support for independence showed great dissatisfaction and that "every politician must now listen to their cry for change".
- By ITV News Political Editor Tom Bradby
David Cameron normally wakes up around 5:30 so he will be up by now and will know that his job has been saved effectively. A lot of Tory MPs in recent months have been saying that if he was the Prime Minister who lost the union he would have to go.
This was an enormous scare for him and the whole of the Westminster village. To be blunt, it was absolutely clear that an awful lot of people in Scotland had concluded that practically anything would be better than being ruled by Westminster.
So there's a lot of deep thinking that needs to go on here. The Prime Minister's immediate task is first of all to say to the Scots: 'We were serious about giving you more devolution.' But also to say to the English: 'Look we understand that that leaves everyone else, and the Welsh and Northern Irish, with constitutional questions. We will address that'.
Deputy Prime Minister Nick Clegg said he was "absolutely delighted" at Scotland's "momentous decision" to remain part of the UK.
Alex Salmond has said he accepts the No verdict of the Scottish people and called on all Scots to do the same.
Scotland's First Minister said the 1.6 million Yes voters was still a "substantial vote for Scottish independence and the future of the country".
As Scotland looks ahead Salmond say they now expected Westminster to honour its pledge of more powers "with rapid force".
There is "a job of work to do" to unite Scotland after the referendum vote exposed a divided nation, the Scottish Secretary has said.
Alistair Carmichael told Good Morning Britain: "There's no getting away from that. There is now a job of work to be done to heal the wounds and to build again the close cooperation that we need to have in Scotland."
Despite the pro-Union No camp winning 55% of the vote, No grabbed a good 45.5%.
Moray voted to remain part of the UK after rejecting independence by 36,935 to 27,232.
Alex Salmond has said that the independence referendum has put a "scare and a fear" into the "heart of the Westminster establishment".
He ended his first speech since yesterday's historic plebiscite saying:
David Cameron has announced he will speak shortly after 7am after Scotland chose to remain part of the UK.
Alex Salmond has pledged to "work constructively" will all parties to secure greater devolution for Scotland.
Referring to pledges from the pro-union parties to give the Scottish Parliament greater powers, he said "Scotland will expect these to be honoured in rapid course".
Scotland's First Minister Alex Salmond has begun by saying "Thank you to Scotland for 1.6 million votes for Scottish independence."
He conceded that Scots voted against independence, saying "I accept that verdict". He called on all of Scotland to accept it as well.