Karadzic is accused of organising the 1995 massacre of more than 7,500 Muslims in Srebrenica and other atrocities in the Bosnian war.
The UN tribunal for the former Yugoslavia confirmed his arrest.
Olga Kravan, of the International Criminal Tribunal for Yugoslavia, told Al Jazeera that Karadzic's initial appearance in front of the judges should occur in the "near future".
He will have to answer to all the charges against him, "including genocide, complicity in genocide, exterminations, murders, and many other crimes", she said.
Karadzic was indicted on genocide charges in 1995 by the UN tribunal, and he topped its most-wanted list for more than a decade.
He was arrested on a public bus around 9:30am on Friday and held until he was brought to the court on Monday, Sveta Vujacic, his lawyer, said.
"[Karadzic] just said that these people showed him a police badge and then he was taken to some place and kept in the room. And that is absolutely against the law what they did," Vujacic said.
|Profile: Radovan Karadzic
|One of the world's most-wanted war crimes fugitives.
Came to power in Bosnia's first democratic elections in 1990.
Accused of masterminding a number of atrocities in Bosian war, including the massacre of 8,000 Muslims in Srebrenica in 1995.
Also accused of organising four year siege of Sarajevo where thousands were killed and brutal ethnic cleansing campaign.
Indicted twice by the UN war crimes tribunal but evaded arrest for 13 years, often reportedly by using elaborate disguises.
US offered a $5m reward for information leading to his capture.
"The judge also said that he will look into this matter, who and why kept him for three days."
Haris Silajdzic, a member of the Bosnian presidency, welcomed the news of Karadzic's arrest.
"This is a big day for international justice," he told Al Jazeera. "It will provide a big relief to the victims".
Silajdzic urged that those killed and exiled by Karadzic be remembered.
In order for "justice to be complete, we must erase the consequences of this genocide in Bosnia", he said.
Serbia has been under heavy pressure from the European Union (EU) to turn over those suspected of involvment in war crimes commited during the 1992-1995 Bosnian war to the UN tribunal in The Hague.
The arrest of Karadzic and other suspected war criminals, is one of the main conditions of Serbian progress towards EU membership.
Javier Solana, the EU's foreign policy chief, described Karadzic's capture as "excellent news."
"The place where Radovan Karadzic belongs is in front of the tribunal in The Hague, having a fair trial and responding to the crimes of which he is accused."
Karadzic is still seen by some fervent Serbian nationalists as a hero following the collapse of Yugoslavia.
Heavily armed Serbian security forces were deployed around the war-crimes court in Belgrade where Karadzic was taken and dozens of Karadzic supporters were reportedly seen gathering near the building chanting "Karadzic Hero!" and "Tadic Traitor!"
Several were arrested after attacking reporters.
Officers were also deployed outside the US embassy which was the target of nationalist protesters after Kosovo declared independence earlier this year.
Aljosa Milenkovic, reporting for Al Jazeera from Serbia, said Karadzic was captured by Serbian special forces inside Serbian territory.
"It's interesting that he has been captured under the new government ... during the previous three or four years the Serbian government said he [Karadzic] was not hiding in Serbia," Milenkovic said.
|Bosnian Muslims have campaigned for justice for Srebrenica victims [EPA]
He said that Karadzic would be questioned by a special court in Serbia and then sent to The Hague.
"We will probably see Mr Karadzic, within seven days, in The Hague tribunal," he said.
Ratko Mladic, his military leader during the Balkans war from 1992 to 1995, is still at large.
Karadzic would be the 44th Serb suspect extradited to the tribunal in The Hague.
The others include former Slobodan Milosevic, the former Serbian president, who was removed from power in 2000 and died in jail in 2006 while on trial on war crimes charges.
Edward Joseph, a Balkans analyst, told Al Jazeera that following Karadzic's arrest, the capture of Mladic - whom he labelled a "major figure" in the war crimes of the 1990s - would be "significant".