Danny Alexander said that was the "UK dividend" for every man, woman and child north of the border.
He spoke out as the UK Treasury published a new report assessing the fiscal position of an independent Scotland over the period from 2016 to 2035/36.
With voters in Scotland due to decide the country's future in September's independence referendum, Mr Alexander argued that leaving the UK would mean lower tax revenues north of the border and increased public spending.
The UK Government minister said a separate Scotland could face higher interest payments on Government debts, at the same time as it had to deal with declining oil revenues and an ageing population.
Speaking on a visit to Edinburgh, Mr Alexander said: "Today we have shown that, by staying together, Scotland's future will be safer, with stronger finances and a more progressive society.
"Because as a United Kingdom we can pool resources and share risks, it means a UK dividend of £1,400 a year for every man, woman and child in Scotland.
"That dividend is our share of a more prosperous future. It is the money that will pay for better public services and a fairer society."
The Treasury said its calculations on the cost of independence had been compiled over 18 months and were "based on independent forecasts and modelling".
The figures represent "the most comprehensive analysis of the fiscal position of Scotland yet produced", Mr Alexander said.
The annual £1,400 UK dividend - which effectively represents the UK Government's figure for the cost of independence - is calculated using a number of components.
The Treasury's analysis says the majority of the dividend comes from higher public spending in Scotland and lower onshore tax revenues at present and by 2016/17, that are not covered by higher oil revenues.
"Over the following 20 years, remaining part of the UK would insure people in Scotland against the fiscal costs of an ageing population and declining oil revenues," according to the analysis.
The UK dividend includes people in Scotland avoiding the direct costs that would come with independence, Mr Alexander said.
These include higher interest rates for an independent state to borrow, the net costs of setting up new institutions, and the net costs of funding the Scottish Government's white paper policies.
Mr Alexander said: "An independent Scotland would have to spend more to deliver the same services as now. So where does that leave us? A worse starting point. The cost of setting up a new state. Unfunded policies. Declining oil revenues and an ageing population.
"All of that, easily avoided by staying within the UK, is worth £1,400 for each person in Scotland for the next 20 years. That's the UK dividend."
Mr Alexander said the £1,400 per person represented 11% of Scotland's total public spending - the equivalent of two-thirds of Scotland's NHS budget, or the whole education budget.
Offsetting the dividend without cutting public spending would involve increasing the basic rate of income tax from 20% to 28%, he said.
Meanwhile VAT would have to be increased from 20% to 26%, with duties on alcohol, tobacco and fuel rising to 40%, he added.
Asked about the affects of negotiations on assets and liabilities on the dividend figure, Mr Alexander said: "Of course assets and liabilities would have to be divided up. I don't think that anybody thinks that process would be to the net benefit or net disadvantage of Scotland or the rest of the UK.
"In terms of financial assets they are included in the net debt calculations in this paper.
"The point in the paper is that once you've done that analysis, there is still a substantial cost to Scotland in setting up new institutions, there is still a substantial cost in terms of the interest rate premium on the debt for Scotland.
"We haven't engaged in any pre-negotiation on that subject, and I think the Scottish Government's claim that somehow the process of negotiation would somehow be to the financial advantage of Scotland, as opposed to something that would be a neutral, objective exercise would be wrong."
Pressed on the wide range of variable factors that have to be taken into account to reach the dividend figure, he added: "In most parts of this analysis what we are offering are low-end estimates of the dividend precisely to account for those sorts of facts."
Mr Alexander also criticised figures produced by the Scottish Government which state that Scotland could be £5 billion a year better off in 15 years' time without having to raise taxes if it became independent.
He described the figure as a "bonus bogus".
"I just think that the figures that have been presented by the Scottish Government are simply not credible," he said.
"It is about time that the Scottish Government came clean with people that there is a significant cost to setting up a new state."
By contrast, the Chief Secretary said his figures were based on the "most robust independent estimates", and "every single one of these figures is independently sourced, independently backed up".
Addressing claims that the Treasury had misrepresented figures from Professor Patrick Dunleavy of the London School of Economics, and Professor Robert Young of the University of Western Ontario, in setting out the costs of setting up a new state, Mr Alexander said: "Professor Dunleavy's estimates do not form any part of the £1.5 billion calculation for the set up costs of independence that are in this paper.
"The source of the figures is Professor Young's analysis...he gives a range.
"When you look at some of the independent estimates for specific costs, such as the Institute for Chartered Accountants in Scotland, just last week they said that the cost of setting up a new tax system alone...would cost £750 million."
Scottish Conservative deputy leader Jackson Carlaw said: "It's clear from the analysis that people in Scotland will enjoy a far more prosperous and secure future as part of the UK.
"The Scottish Government can't even tell us what the start-up costs of an independent Scotland would be.
"Until the SNP can come up with some hard and fast facts, the public will see through their pie-in-the-sky pledges."