Police sealed the street outside the City of Westminster magistrates court as a black unmarked car carrying several police officers and a silver-haired man believed to be the 39-year-old Australian raced into the car park.
A court official said the extradition hearing was due to start at 1400 GMT and confirmed that Assange had arrived.
Outside court, his London-based lawyer Mark Stephens said that Assange was "fine" after he surrendered to Scotland Yard's extradition unit at a police station in the capital on Tuesday morning.
"It was very cordial. They have verified his identity. They are satisfied he is the real Julian Assange and we are ready to go into court," Stephens told reporters.
Assange's lawyers have said they will fight all attempts to extradite him to Sweden. The legal process could take weeks or even months.
Stephens did not say whether Assange would seek bail, but police sources said he may not be granted it because of the risk that he will try to flee the country.
Assange was arrested on a European arrest warrant issued by Sweden over allegations of unlawful coercion, sexual molestation and rape, the Metropolitan Police said.
He has denied the charges, with his lawyers saying they could be "politically motivated" following the release by WikiLeaks of thousands of secret US documents.
