Lawyers for the WikiLeaks founder had argued that the warrant should be dismissed because it had "lost its goal and function" after the investigation over sex-related allegations was dropped previous year.
Julian Assange skipped bail conditions to avoid extradiction to Sweden where he was facinga rape allegation which he denied, though the case has been dropped.
Assange's lawyer Mark Summers asked Judge Arbuthnot to consider whether it would be in the public interest to continue pursuing his client for breach of bail.
Ahead of Tuesday's ruling, a small group of Assange supporters gathered outside the court in central London.
Despite arguments from Assange's lawyers that the dropped charges in Sweden make the British arrest warrant unnecessary, senior district judge Arbuthnot stated, "Having considered the arguments ..."More news: Liverpool trio set to feature for U-23s
The 46-year-old former hacker claims he feared authorities would hand him over to the U.S. to face prosecution over the leak of classified military and diplomatic documents.
Swedish prosecutors dropped the case past year, saying all possible leads had been "exhausted". A decision in Assange's favor would end Britain's case against him.
He also cited a United Nations report in support of Assange.
US Attorney General Jeff Sessions previous year said his arrest was a "priority".
USA officials haven't confirmed whether a request for Assange's extradition has been made.
A prosecutor did however say that if Assange is ever passing through Sweden, he should still pop in.
She told the court that not surrendering to bail was a stand-alone offence under the Bail Act and Mr Assange must explain why he had failed to do so.