The Chancellor, making his first detailed statement since the outcome of the referendum was revealed on Friday, said that the regulators had been working on contingency plans in case of a Brexit vote.
He said he stood by his comments about warnings made during the campaign about the adverse effect of exiting the EU but stressed the Government was prepared to handle the situation.
He insisted the country’s economy was strong and able to withstand the shock.
He said: “It is inevitable, after Thursday’s vote, that Britain’s economy is going to have to adjust to the new situation we find ourselves in.
“In the analysis that the Treasury and other independent organisations produced, three particular challenges were identified – and I want to say how we meet all three.
“First, there is the volatility we have seen and are likely to continue to see in financial markets.
“Those markets may not have been expecting the referendum result – but the Treasury, the Bank of England, and the Financial Conduct Authority have spent the last few months putting in place robust contingency plans for the immediate financial aftermath in the event of this result.
“We and the PRA have worked systematically with each major financial institution in recent weeks to make sure they were ready to deal with the consequences of a vote to leave.”
Mr Osborne explained that he and Mark Carney, Governor of the Bank of England have discussed a co-ordinated response with other major economies in calls on Friday with the Finance Ministers and Central Bank Governors of the G7.
He revealed there are “further well-thought-through contingency plans if they are needed”.
He said: “It will not be plain sailing in the days ahead. But let me be clear. You should not underestimate our resolve. We were prepared for the unexpected. We are equipped for whatever happens.
“And we are determined that unlike eight years ago, Britain’s financial system will help our country deal with any shocks and dampen them – not contribute to those shocks or make them worse.”
His message to businesses was that the British economy is “fundamentally strong, we are highly competitive and we are open for business”.
He added that he has been in contact with fellow European finance ministers, central bank governors, the managing director of the IMF, the US Treasury Secretary and the Speaker of Congress, and the CEOs of some of major financial institutions in the last 72 hours I have “so that collectively we keep a close eye on developments”.