Mark Carney told MPs pursuing EU membership would result in an independent Scotland having to commit to joining the euro "in the fullness of time", meaning any other arrangement such as Alex Salmond's preferred currency union - ruled out by Westminster - would be only a temporary arrangement.
Appearing before the Commons Treasury Committee, Mr Carney also stressed how an independent Scotland would need currency reserves many times the size of its GDP to withstand the pressures from international markets.
Asked if RBS would have to move to the remaining UK if an independent Scotland joined the EU, the Governor replied: "It's a distinct possibility but I shouldn't prejudge it. It depends on their arrangements."
His remarks came in the context of recent reports about how EU rules required banks to have their HQs in the countries where most of their customers lived; in the case of RBS, this would be England.
Asked if Scotland would need to establish its own currency before joining the euro or if it could apply to join straight away, Mr Carney said "any new application to join the European Union would include a commitment to join the euro in the fullness of time".
The First Minister maintains a currency union is the SNP Government's preferred option despite all three main Westminster parties saying it will not happen. One Whitehall source insisted the idea was now "dead".
In January, the Governor made clear in a speech in Edinburgh that an effective currency union would force a newly-independent Scotland to cede some national sovereignty to London.
Yesterday, he stressed that he would not judge whether a currency union should happen or not but warned the option of so-called sterlingisation - Scotland continuing to use the pound in the absence of a currency union - would leave it without the insurance of a lender of last resort. He said that with a curr-ency union the Bank's services currently provided to Scotland would be "passported over" while, without one, each service would have to be reviewed.
But the Governor agreed a currency union or sterlingisation would be tested by the markets because it "would be seen as a temporary arrangement" and this would mean Scotland would need substantial currency reserves to withstand the pressure.
Asked if £6 billion of reserves would suffice, he pointed to the example of Hong Kong, which had reserves "multiple times the size of its GDP; £6bn is not multiple times Scotland's GDP".
The Governor also noted how viability within a currency union was "a bit like being pregnant. You can't be half viable in a currency union; you need all the components".
A Better Together spokesman said what people in Scotland needed was clarity from Alex Salmond about his Plan B for what would replace the pound.
But Stewart Hosie for the SNP, who sits on the Treasury Committee, said he was pleased by Mr Carney's confirmation about the Bank's "neutrality on the issue of Scottish independence and that his Edinburgh speech was a technical assessment of currency unions not a judgment on independence".
l A major Scottish investor has said independence could lead to prolonged uncertainty. Edinburgh-based Murray International Trust, an investment arm of Aberdeen Asset Management, states in its financial report: "The company is registered in Scotland and the board is mindful that there is uncertainty arising in relation to the referendum on Scottish independence."