A record 84.5% of the electorate made their way to polling stations to make their voices heard.
The previous highest turnout in any UK election was 83.9% in the 1950 general election. Turnout at the last Holyrood election in 2011 just scraped above 50%.
While Glasgow voted in favour, the margin of victory was not large enough to give Alex Salmond and his campaign the momentum they need.
His deputy Nicola Sturgeon conceded defeat with a handful of results still to be declared.
The Deputy First Minister said there was a “real sense of disappointment that we have fallen narrowly short of securing a Yes vote”.
Mr Salmond had been expected to make an appearance at the count at the Aberdeen Exhibition and Conference Centre but did not arrive, flying straight to Edinburgh before it was announced that voters in his constituency of Aberdeenshire had resoundingly rejected independence by 60.3% to 39.6%.
Sir Malcolm said: “This is the SNP’s backyard, it’s Alex Salmond’s backyard. He didn’t have the guts to come to his own count in his own area because he knew he had been comprehensively rejected.”
Apart from Glasgow, there were wins for Yes in only three other of Scotland’s 32 local authority areas – Dundee, West Dunbartonshire and North Lanarkshire – and damaging losses in other SNP strongholds like Perth & Kinross, Angus and Moray.
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%.
No won convincingly in Edinburgh and the result in Fife – where 114,148 voted Yes and 139,788 No – made the result a mathematical certainty.
In an early-morning phone call, Prime Minister David Cameron spoke to former Labour chancellor Alistair Darling, the leader of the cross-party Better Together campaign, to congratulate him on “a well-fought campaign”.
Deputy Prime Minister Nick Clegg said: “I’m absolutely delighted the Scottish people have taken this momentous decision to safeguard our family of nations for future generations.
“In a dangerous and uncertain world I have no doubt we are stronger, safer, and more prosperous together than we ever could be apart.
“But a vote against independence was clearly not a vote against change and we must now deliver on time and in full the radical package of newly devolved powers to Scotland.
“At the same time, this referendum north of the border has led to demand for constitutional reform across the United Kingdom as people south of the border also want more control and freedom in their own hands rather than power being hoarded in Westminster.
“So this referendum marks not only a new chapter for Scotland within the UK but also wider constitutional reform across the Union.”