Sir George Mathewson, a former RBS chief executive and chairman, argued that financial services in Scotland had been "neglected by the Westminster government and its London-centric policy".
He also claimed that banks such as RBS and Lloyds could "scarcely be described as Scottish banks", adding that if there was a Yes vote in next month's referendum it should be the rest of the UK government that should be primarily responsible for dealing with the situation.
Sir George also gave his backing to Scottish Government plans for a currency union with the rest of the UK to be established if there is a Yes vote on September 18, allowing an independent Scotland to continue to use the pound.
These proposals have already been dismissed by the three main Westminster parties and last week First Minister Alex Salmond was accused of a ''huge deception'' over his plan.
Sir Martin Jacomb, the former chairman of Prudential, and Sir Andrew Large, a former deputy governor of the Bank of England, said that a currency union is ''not compatible with Scotland being politically independent and is therefore not on offer''.
But in a piece in the Financial Times, Sir George said those who argued against a currency union "ignore the interconnected nature of our financial systems".
He stated: "As the debate over Scottish independence enters its final stage, careful analysis is giving the lie to the unionists' scaremongering about the consequences of independence. For Scotland's financial sector, this is an opportunity, not a threat."
Sir George continued: "It is nonsense to argue that Scotland's banking sector would make independence impossible to achieve.
"Banks such as RBS and Lloyds Banking Group have strong Scottish connections but they can scarcely be described as Scottish banks.
"In reality they are run from London, and that is where they are regulated. The customers, assets and ownership are global, even if the holding company happens to be registered in Edinburgh.
"The location of a brass plate bearing the name of a bank may determine where the institution formally resides. But it does not tell you which government is primarily responsible for overseeing the bank or for limiting the damage if things go wrong.
"That depends principally on where the bank's economic assets are located - which is, after all, the place most at risk from contagion in the event of a banking crisis.
"In the case of RBS and Lloyds, which have substantial operations throughout the UK, the answer is clear. The UK Government already owns significant chunks of both institutions; 80%, in the case of RBS."
He argued that "independence will bring new opportunities for Scotland's financial sector - which is one of the country's strengths, though it is neglected by the Westminster government and its London-centric policy".
Sir George said: "Scotland can support and expand the financial services sector using the powers of independence to attract new businesses and new entrants to the market.
"It will build on successes such as Virgin Money and Tesco Bank, both of which have operations in Scotland. A competitive and efficient tax system would help Scotland compete with other European financial capitals.
"All of this can and should be achieved in a currency union with the UK, under a common regulatory framework. Those who argue that this is impossible ignore the interconnected nature of our financial systems."
He concluded: "The Scottish Government's proposals for the economic governance of an independent Scotland are undoubtedly the best on the table.
"They offer a bright future for Scottish financial services and the wider economy. The alternative claims of those with a political interest in Scotland voting No should be taken with a bucket of salt."
A spokesman for Better Together, the main pro-UK campaign group, said: "As an adviser to Yes Scotland, Sir George Mathewson should tell us what the nationalists' plan B for replacing the pound in a separate Scotland is.
"There would not be a currency union if we leave the UK. It wouldn't be good for Scotland and it wouldn't be good for the continuing UK. In tomorrow's TV debate Alex Salmond must give the Scottish people some honest answers about the consequences of separation for our currency.
"The usual bluff and bluster simply won't do. Would we rush to adopt the Euro? Or would we set an unproven separate currency? The idea that voters can go to the polls blind on this fundamental issue isn't credible."
SNP MSP Kenneth Gibson, convener of Holyrood's Finance Committee, said: "Since the launch of the No campaign two years ago, Alistair Darling and his Tory allies have tried relentlessly to spread fear about Scotland's financial sector - but this expert intervention from Sir George Mathewson disproves the tired old scaremongering once and for all.
"Sir George is absolutely right to say that the No camp's claims need to be taken with a bucket of salt - people in Scotland just don't believe their predictions of doom and gloom any more.
"As Sir George makes clear, with a Yes vote we can use the economic powers of independence to further grow our financial sector and attract new business to Scotland - and to have an economic policy tailored to Scotland's needs, rather than London and the south-east."