An independent Scottish Government would become responsible for a "fair and proportionate" share of current liabilities, according to a paper issued by the Treasury.
In the event of independence, a new contract would be needed between governments following extensive negotiations.
There would be no change to UK-issued gilts, or bonds.
"Instead, an independent Scotland would need to raise funds in order to reimburse the continuing UK for this share," the Treasury paper states.
British ministers have so far refused publicly to "pre-negotiate" terms of independence for Scotland.
Voters in Scotland will be asked whether the country should be independent in a referendum on September 18.
The Treasury paper states: "In the event of Scottish independence from the United Kingdom, the continuing UK Government would in all circumstances honour the contractual terms of the debt issued by the UK Government.
"An independent Scottish state would become responsible for a fair and proportionate share of the UK's current liabilities, but a share of the outstanding stock of debt instruments that have been issued by the UK would not be transferred to Scotland.
"For example, there would be no change in counterparty for holders of UK gilts. Instead, an independent Scotland would need to raise funds in order to reimburse the continuing UK for this share."
Official statistics show public-sector gross debt stood at £1.38 trillion by the end of 2012-13.
"In the event of independence, the full spectrum of assets and liabilities - past, future and contingent - would need to be considered in negotiations between the continuing UK and Scottish Governments, on a case-by-case basis," the report states.
"This means that the negotiations would need to cover the arrangements for all forms of debt covered in this note, not just gilts and Treasury bills."
The decision by the Treasury shows that UK ministers are coming to terms with "reality", according to Scotland's First Minister, Alex Salmond.
He had previously suggested that Scotland would be entitled to refuse to take on debt if the UK continued to rule out discussion on sharing assets such as the pound sterling.
"These documents make clear that we remain prepared to negotiate taking responsibility for financing a fair share of the debts of the UK provided, of course, Scotland secures a fair share of the assets, including the monetary assets," Mr Salmond said.
"Any market uncertainty in the gilts market has been caused by their own refusal to discuss the terms of independence before the referendum and it is their own insistence that Scotland would be a new state that lands them with the unambiguous legal title to the accumulated debts of the United Kingdom.
"That position is now beyond argument and today's announcement makes clear that Scotland would be in an extremely strong negotiating position to secure that fair deal."
The UK Government and Better Together campaign group should stop the "bluff and bluster", he added.
"On the issue of the currency, for example, they should listen to the overwhelming majority of the people of England who, polls indicate, see the common sense of sharing a common currency.
"The people know that it would be in the interests of both Scotland and the rest of the UK to do so, that it would be logical and desirable, as Alistair Darling said last year before he got caught up in campaign fever."
The Scottish Government set out two possible positions on debt sharing in its formal White Paper on independence last November.
It explored the historical balance of public spending and tax since 1980, when figures became available, or a population-based share.
"Negotiations will also take into account the degree to which Scotland's share of UK public sector debt, and in turn its annual debt interest payments, could be reduced in return for forgoing rights to certain UK assets," the White Paper states.
It calculates a historical share of debt interest could be £3.9 billion in 2016-17 or £5.5 billion based on a per head share.
Treasury Secretary Danny Alexander said the UK Government's new position should reassure the financial markets.
"We want to make sure people who lend us money continue to do so at very low interest rates," he told BBC News.
"Everybody knows that an independent Scotland would be likely to face considerably higher interest rates, less credibility in the international finance markets.
"What we want to avoid is any sort of idea that the rest of the UK - taxpayers across the whole of the UK, including in Scotland between now and in September - pay any sort of separation surcharge, an extra cost on debt that causes uncertainty in the financial markets.
"But an independent Scotland would still be required to take its fare share of the debt, were Scotland to vote to separate from the rest of the UK."
An independent Scotland should want to be credible in the markets, he said.
"The worst thing in the world, I think, for an independent Scotland, would be to start its life as a new state - in the unlikely event that it is created - with a default on its debt obligations."
Prime Minister David Cameron's official spokesman told a Westminster media briefing: "Both the UK Government and the Scottish Government have already said that in the event of Scottish independence - which is something that the PM and those who share his position will be continuing to argue against - an independent Scottish state would become responsible for a fair and proportionate share of the UK's liabilities.
"What the Treasury is doing today is providing clarification for investors. In the unique circumstances of the independence campaign, it is right to do what we need to at a technical level to ensure UK credibility and confidence in the debt management operations."
Asked what leverage the rump UK would have to ensure that Scotland paid its share of liabilities in the case of independence, the PM's spokesman said: "In the event of a Yes (vote), there would have to be bilateral negotiations involving the UK Government and the Scottish Government.
"We are not going to get into a pre-negotiation. I'm sure that those on the other side of the argument may want to try to drag us into that, but it is not what we are going to do."