Mr Assange, 46, fled to the embassy after skipping bail to avoid being sent to Sweden to face an allegation of rape, which he denied. The Swedish case was dropped in May last year, but Britain still has a warrant for his arrest over the breach of bail terms.
Mr Assange has not left the embassy since he first walked in nearly six years ago and his lawyers had argued in a court hearing last week that it was no longer in the interests of justice for British authorities to seek to arrest and prosecute him for skipping bail.
"Having weighed up the factors for and against ... I find arrest is a proportionate response even though Mr Assange has restricted his own freedom for a number of years," judge Emma Arbuthnot said in her ruling at Westminster Magistrates Court.
"Defendants on bail up and down the country, and requested persons facing extradition, come to court to face the consequences of their own choices. He should have the courage to do so too," she said.
(Reporting by Andrew MacAskill, writing by Estelle Shirbon; editing by Stephen Addison)