Two weeks ago the Supreme Court rejected his argument that a European arrest warrant for extradition was invalid, but his lawyers had argued that some of the judges had reached their decision based on a legal point that had not been argued in court.
In a statement, the court said all seven judges had agreed the application made on behalf of the self-styled anti-secrecy campaigner was without merit.
"The Court has ordered that, with the agreement of the respondent ... the required period for extradition shall not commence until the 14th day after today," it added.
Assange, who denies any wrongdoing in Sweden, could still take his case to the European Court of Human Rights (ECHR), a move which could hold up the extradition.
Swedish prosecutors want to question Assange over allegations of rape and sexual assault made by two female former WikiLeaks volunteers. He has been fighting a legal battle against extradition since his arrest in Britain in December 2010.
The former computer hacker gained international prominence in 2010 when WikiLeaks began releasing secret video footage and thousands of confidential US diplomatic cables, many of them about Iraq and Afghanistan, in the largest leak of classified documents in US history.
That made him a hero to anti-censorship campaigners, but Washington was furious about the release of classified documents.
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