In a UK Government article, co-written with Treasury Chief Secretary Danny Alexander, Mr Osborne said that a currency union could only work as part of a political and economic union.
They also said Scotland could "of course" be independent, but that remaining in the UK is the best way to "realise aspirations".
It comes ahead of the publication on Tuesday of the UK Government's analysis of the implications for the currency of Scottish independence.
But the First Minister said the Chancellor has lost "all remaining economic credibility".
Mr Salmond said: "He has been downgraded by a second credit agency which once he boasted about.
"He has spent the last week bickering with IMF economists whose support he once lauded. He will spend the next week with the UK economy teetering on the brink of a double dip recession.
"He is a downgraded Chancellor without a remaining shred of credibility. This is the man who had the audacity to come to Scotland 18 months ago to sneer that the constitutional debate would damage the economy.
"The reality is that Scotland is outperforming the UK on every measure - inward investment, employment, unemployment and growth.
"However we are well aware that it is George Osborne who has the capacity to damage Scotland's recovery unless he changes course now. We do not want to see more Scottish jobs sacrificed by Chancellor downgrade."
The Scottish Government has set out plans to retain the pound as Scotland's currency if the country votes for independence in next year's referendum, in what the First Minister has described as a "sterling zone" with the rest of the UK.
Economics experts in the Fiscal Commission Working Group, set up by Mr Salmond, have already concluded keeping sterling as the currency in an independent Scotland was "sensible" and an attractive choice for the rest of the UK.
In their article, Mr Osborne and Mr Alexander wrote: "This isn't a question of whether or not Scotland could go it alone - of course Scotland could.
"The real question is whether going it alone is the best way for people living in Scotland to realise their aspirations and provide security for themselves and their family.
"We hope very much that people living in Scotland will decide to stay. The United Kingdom has done so much together and can achieve so much more in the future.
"For the advocates of independence the United Kingdom doesn't work. For them all the risk and uncertainty of separation is worth it just to have control of all the decisions of a fully sovereign state. But they're tying themselves in knots.
"They know in their heart of hearts that the economic and political union we have across the UK does work. And that a formal currency union can only work with political and economic union.
"Scottish Government ministers have made it clear that they want an independent Scotland to keep the pound, the Bank of England and to enter a formal currency union with the rest of the UK.
"So if Scotland does vote Yes on 18th September 2014, they say they want to hand, to what would become a foreign government, key decisions over the Scottish economy.
"This is one of the big contradictions in their whole economic approach. Campaigning to 'bring powers home' with one hand, while giving them away with the other. Calling for 'full fiscal freedom' with one breath, but calling for a 'full fiscal pact' with the next. It simply doesn't add up."
The senior UK Government figures said the UK is a "deeply integrated" single domestic market with a large percentage of Scottish exports being done with the rest of the UK and thousands of people working for the same companies across borders.
"We can understand why the proponents of independence wish a separate Scotland to enter into a formal currency union with the rest of the UK," they wrote.
"But many of their own experts disagree with them. It is not as simple and straightforward as Scottish Government ministers pretend it is.
"The conclusion is clear. The pound we share now works and it works well. Under independence all the alternatives are second best. So our question to the nationalists - are you really saying second best is good enough for Scotland?
"For us the answer is clear. We want the best for Scotland and for all of our United Kingdom."
Deputy First Minister Nicola Sturgeon said maintaining the pound in an independent Scotland was the "common sense position supported by the facts".
"The combination - which only comes with independence - of keeping the pound, accessing Scotland's abundant resources, and taking decisions on tax and other economic policies that are right for Scotland, is the best way to boost jobs and growth," she said.
"Scotland's finances are consistently stronger than the UK's - generating more revenue per head than the rest of the UK in each one of the past 30 years - and Scotland has had a lower fiscal deficit than the UK over the past five years.
"Next year's vote is the choice between unlocking the opportunities independence will open up with a Yes vote, or continuing to allow economic and welfare policy to be set by a Westminster system that isn't working for Scotland."
Alistair Darling, leader of the Better Together campaign, said the SNP were cornering themselves between handing economic control over an independent Scotland to London or creating a Scottish currency.
The former Labour Chancellor, said the nationalists' contortions on economic and monetary policy lacked credibility.
He said: "The economy is going to be absolutely central to this debate about independence and central to the economy is the currency we use.
"In the space of about 12 months, the nationalists have gone from adopting the euro - which is about as popular in Scotland as it is anywhere else in the UK - to simply using the pound like Panama uses the US dollar.
"That would be disastrous... so they are now saying they want a currency union. But they don't seem to understand if you have a currency union, there are terms and conditions about your taxation, about your borrowing, about your spending.
"Whatever else that is, it is not independence."
Mr Darling, who was speaking on the Sky News Murnaghan programme, added: "Unless they are prepared to say now they will sign up to whatever constraints, whatever straight jacket this currency union imposes, they cannot guarantee to keep the pound and they are driven back to what a number of them are recently talking about, which is having a separate Scottish currency."