George Osborne has said the UK is ready to face the future "from a position of strength" and indicated there will be no immediate emergency Budget.
He said there would still need to be an "adjustment" in the UK economy.
However, it was "perfectly sensible to wait for a new prime minister" before taking any such action.
He also said that only the UK could begin the process of leaving the EU by triggering Article 50 of the Lisbon Treaty.
The chancellor made the comments in a statement aimed at calming financial markets after the Brexit vote triggered market turmoil on Friday.
He had not spoken since the Leave campaign won Thursday's referendum.
"I said we had to fix the roof so we were prepared for whatever the future held and thank goodness we did," he said.
On the process of the UK's departure from the EU, he said: "Only the UK can trigger Article 50. And in my judgement, we should only do that when there is a clear view about what new arrangements we are seeking with our European neighbours.
"In the meantime, during the negotiations that will follow, there will be no change to people's rights to travel and work and to the way our goods and services are traded or to the way our economy and financial system is regulated."
The chancellor's statement came as the repercussions of the Brexit vote continued to shake the UK's political system.
The opposition Labour party has seen 14 of its senior members resign since shadow foreign secretary Hilary Benn was sacked in the early hours of Sunday after he told Mr Corbyn he had lost confidence in him.
The latest front-bench resignations, on Monday morning, are by shadow foreign minister Diana Johnson, shadow civil society minister Anna Turley and shadow defence minister Toby Perkins.
In response, Labour leader Jeremy Corbyn has announced a reshaped shadow cabinet, but he still faces a potential no-confidence motion from Labour MPs.
At the same time, Boris Johnson, widely seen as the most likely successor to Prime Minister David Cameron, has said the UK will continue to "intensify" co-operation with the EU following the country's vote to leave.
The leading pro-Leave campaigner said exit supporters had to accept that the 52-48 result was "not entirely overwhelming".
Before the chancellor's statement, the pound fell further in trading in Asia, down another 2.6% against the dollar at $1.34.
In early trading on the London stock market, the benchmark FTSE 100 index fell nearly 1% before recovering some of the lost ground.
Mr Osborne said he had spoken to Bank of England governor Mark Carney and that there were "well thought through contingency plans if needed".
He said he had also been co-ordinating with fellow finance ministers in Europe, the International Monetary Fund, central banks and the US Treasury Secretary to help markets cope with the shock.
"You should not underestimate our resolve," he said.
Mr Osborne said the referendum result was "not the outcome that I wanted", but added: "The British people have given us their instructions."
He also appeared to rule out resigning in the near future, saying that the UK needed to negotiate its exit from the EU with its "European partners and allies".
"I intend to play an active part in that debate," he said.