Former Bosnian Serb leader Radovan Karadzic may not be taken to prison in The Hague until next week.
Karadzic, who evaded capture for almost 13 years, faces charges of genocide relating to the war in the former Yugoslavia during the 1990s.
His lawyer Sveta Vujacic say he will appeal against his extradition. He has three days to do so.
Serb officials say Karadzic, one of the world's most wanted men, was living under false papers in Serbia's capital, Belgrade. He was practising alternative medicine.
The Serbian minister for relations with The Hague tribunal, Rasim Ljajic, said Karadzic was sporting a long white beard and calling himself Dragan Dabic.
He told a news conference in Belgrade that Karadzic was using false papers and working in a private practice.
The United Nations says Karadzic's forces killed up to 8000 Bosnian men and boys from Srebrenica in July 1995 as part of a campaign to "terrorise and demoralise the Bosnian Muslim and Bosnian Croat population".
He was also charged over the shelling of Sarajevo, and the use of 284 UN peacekeepers as human shields in May and June 1995.
Serbia's war crimes prosecutor, Vladimir Vukcevic, said Karadzic had "walked around freely, even appeared in public places. The people who rented him the apartment did not know his true identity".
He gave public lectures and was a regular contributor to a magazine called Healthy Life, according to its editor Goran Kojic.
He said Karadzic was a "highly cultured man", "very tolerant", "very intellectual" and "a great person".
Mr Kojic added that he never talked politics with Mr Karadzic. Their conversations were limited to health.
Karadzic was last seen in public in eastern Bosnia in 1996, and was previously thought to have hidden in Serb-controlled parts of Bosnia, as well as in Montenegro and Serbia.
His arrest is one of the main conditions of Serbian progress towards European Union membership.
The United States and European Union have urged Serbia to follow up the arrest of Karadzic by apprehending his wartime commander Ratko Mladic as quickly as possible.
Karadzic was a close ally of former Yugoslav president Slobodan Milosevic, who was himself extradited to The Hague tribunal in 2001, but died in 2006, shortly before a verdict was due to be delivered in his case.
Former United States assistant secretary of state for Europe, Richard Holbrooke, welcomed his capture, describing him as the "Osama bin Laden of Europe".