failed in his appeal against extradition from the UK to Sweden over allegations of rape and sexual assault.
Two judges at the High Court in London decided that a previous ruling in favour of extradition must be upheld.
Swedish authorities want him to answer accusations of raping one woman and sexually molesting and coercing another in Stockholm last year.
Mr Assange's lawyers say they will appeal at the Supreme Court.
They have 14 days to bring the case to the highest court in the land, on the grounds that it raises issues of general public importance.
However, Mr Assange's legal team will first need to seek permission from the High Court to launch the appeal.
In February, District Judge Howard Riddle ruled that Mr Assange should be extradited to face investigation following a hearing at City of Westminster Magistrates' Court.
The 40-year-old Australian denies the allegations and says they are politically motivated.
However, in their ruling the judges, the President of the Queen's Bench Division Sir John Thomas, sitting with Mr Justice Ouseley, said that the issuing of the European arrest warrant (EAW) that led to Mr Assange's arrest and all subsequent proceedings to achieve extradition was "lawful" and "proportionate".
They dismissed Mr Assange's argument that the warrant was invalid because it had been issued by a prosecutor, and not a "judicial authority".
They also said the action of the prosecutor was subject to the independent scrutiny of Swedish judges, "which, as judges of another (EU) member state, we must respect".
The judges said: "It is clear that the allegation is that he had sexual intercourse with her when she was not in a position to consent and so he could not have had any reasonable belief that she did."
The court also rejected Assange's assertion that the descriptions of the offences were not a fair and accurate description of the conduct alleged against him.
They added: "This is self evidently not a case relating to a trivial offence, but to serious sexual offences.
"Assuming proportionality is a requirement, it is difficult to see what real scope there is for the [appeal] argument in circumstances where a Swedish Court of Appeal has taken the view, as part of Swedish procedure, that an arrest is necessary."
'Level playing field'
Wikileaks has published a mass of leaked diplomatic cables which have embarrassed several governments and international businesses.
American soldier Bradley Manning is being held in US custody for allegedly leaking information to the website.
Mr Assange appeared in court wearing a smart suit and Remembrance Day poppy but sat silently through the judgement, said BBC News home affairs correspondent Dominic Casciani.
Upon his arrival, Mr Assange was mobbed and police redirected him away from the crowd who had fixed to the iron railings of the court banners reading "Free Assange! Free Manning! End the wars".
Speaking after the appeal hearing, his supporters outside the court said they were "outraged" by the judges' decision.
Ciaron O'Reilly, 51, said: "Assange is probably the most amazing person in recent history who's upset so many powerful people in such a short space of time so it's obviously not a level playing field."
LONDEN - Julian Assange van onthullingssite WikiLeaks kan bij het Britse hooggerechtshof in beroep gaan om uitwijzing naar Zweden te voorkomen.
Dat heeft de Britse Hoge Raad maandag bepaald.
Assange vreest dat het Scandinavische land hem zal uitleveren aan de Verenigde Staten, waar hij door de onthulling van geheime Amerikaanse overheidsdocumenten via WikiLeaks veel vijanden heeft gemaakt.
Assange wordt in Zweden verdacht van seksuele misdrijven. Hij zegt dat de beschuldigingen politiek gemotiveerd zijn.
Een rechtbank bepaalde begin november dat Assange mag worden uitgeleverd. Hij heeft nu twee weken de tijd om bij het hooggerechtshof in beroep te gaan. Als hij dat doet, zal hij oud en nieuw nog in Groot-Brittannië kunnen vieren.
De 40-jarige Australiër werd vorig jaar gearresteerd, nadat WikiLeaks duizenden geheime documenten van Amerikaanse diplomaten had gepubliceerd.