The surprise decision to leave the EU sparked the resignation of Prime Minister David Cameron, who had backed the unsuccessful Remain campaign -- but has left the activation of Article 50, which triggers the departure, to his successor.
"The prime minister has given us time as a country to decide what that the relationship should be by delaying the decision to trigger the Article 50 procedure until there is a new prime minister in place for the autumn," Osborne said in his first public comments since the result.
The remarks, given at a Treasury press conference in central London, were timed to calm investor jitters ahead of the opening of European stock markets at 0700 GMT.
The London stock market opened down by 0.8%, however.
"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 arrangement we are seeking with our European neighbours," he added.
"In the meantime, and 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," he said.
Chancellor of the Exchequer Osborne expressed confidence that the British economy was strong enough to withstand the fallout from its EU exit.
"Britain is ready to confront what the future holds for us from a position of strength," he added.
Britons cast aside warnings of isolation and economic disaster to vote 52% to 48% in favour of quitting the EU in Thursday's vote.
"On Thursday, the people of the United Kingdom voted to leave the European Union," Osborne added
"That is not the outcome that I wanted or that I threw everything into campaigning for. Now the people have spoken and we, in this democracy, must all accept that result and deliver on their instructions," he said.
He said he was not rowing back from the "concerns I expressed during the campaign" but added, "I fully accept the result of the referendum and will do everything I can to make it work for Britain."
He cautioned however that it was "inevitable" that Britain's economy would "have to adjust to the new situation we find ourselves in".
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