Karadzic is accused of masterminding mass killings that the U.N. war crimes tribunal described as "scenes from hell, written on the darkest pages of human history."
He is accused of organizing the 1995 massacre of 8,000 Muslims in Srebrenica and other atrocities of the Bosnian war.
"I was informed by our colleagues in Belgrade about the successful operation which resulted in the arrest of Radovan Karadzic," the tribunal's head prosecutor, Serge Brammertz, said.
President Boris Tadic's office said Karadzic has been taken before the investigative judge of Serbia's war crimes court.
The fugitive's wife, Ljiljana, told The Associated Press by phone from her home in Karadzic's former stronghold, Pale, near Sarajevo that her daughter Sonja had called her before midnight.
"As the phone rang, I knew something was wrong. I'm shocked. Confused. At least now, we know he is alive," Ljiljana Karadzic said, declining further comment.
Karadzic was indicted on genocide charges in 1995 by the tribunal, and topped the its most-wanted list for more than a decade, allegedly resorting to elaborate disguises to elude authorities.
Serbia has been under heavy pressure from the European Union to turn over suspects to the international tribunal.
Tadic's office said in a statement that Karadzic was arrested "in an action by the Serbian security services."
The White House praised the Serbian government for cooperating with the international tribunal.
"This operation is an important demonstration of the Serbian Government's determination to honor its commitment to cooperate with the International Criminal Tribunal for the former Yugoslavia," said White House Press Secretary Dana Perino. "The timing of the arrest, only days after the commemoration of the massacre of over 7,000 Bosnians in Srebrenica, is particularly appropriate, as there is no better tribute to the victims of the war's atrocities than bringing their perpetrators to justice."
If Karadzic is extradited to the tribunal in The Hague, he would be the 44th Serb suspect extradited to the tribunal. The others include former President Slobodan Milosevic, who was ousted in 2000 and died in 2006 while on trial on war crimes charges.
"This is a very important day for the victims who have waited for this arrest for over a decade. It is also an important day for international justice because it clearly demonstrates that nobody is beyond the reach of the law and that sooner or later all fugitives will be brought to justice," Brammertz said.
The European Union said the arrest "illustrates the commitment of the new Belgrade government to contributing to peace and stability in the Balkans region."
A statement from the EU presidency, currently held by France, said the arrest was "an important step on the path to the rapprochement of Serbia with the European Union."
Karadzic has been a fugitive since he was indicted in July 1995. Charges against him include genocide, murder, inhumane acts, and other crimes committed during the 1992-1995 war.
His indictment alleges that he, acting together with others, committed the crimes to secure control of areas of Bosnia which had been proclaimed part of the "Serbian Republic" and significantly reducing its non-Serb population.
Karadzic's reported hide-outs included Serbian Orthodox monasteries and refurbished mountain caves in remote eastern Bosnia. Some newspaper reports said he had at times disguised himself as a priest by shaving off his trademark silver mane and donning a brown cassock.
As leader of Bosnia's Serbs, Karadzic hobnobbed with international negotiators and his interviews were top news items during the 3½-year Bosnian war, set off when a government dominated by Slavic Muslims and Croats declared independence from Yugoslavia in 1992.
But his life changed by the time the war ended in late 1995 with an estimated 250,000 people dead and another 1.8 million driven from their homes. He was indicted twice by the U.N. tribunal on genocide charges stemming from his alleged crimes against Bosnia's Muslims and Croats.
Under the indictment, last amended in May 2000, the U.N. war crimes tribunal charged former Bosnian Serb leader Radovan Karadzic with 15 counts of genocide, war crimes, crimes against humanity and other atrocities committed between 1992 to 1996.
Those counts include six counts of genocide and complicity in genocide; two counts of crimes against humanity and two counts of deportations and other inhumane acts; and one count each of persecution, inflicting terror on civilians, taking hostages, violating laws of war and gravely breaching the Geneva Conventions
Last month, Serb authorities turned over to The Hague ex-Bosnian Serb police chief, Stojan Zupljanin, who was arrested in the town of Pancevo after nine years on the run.
On Monday, Zupljanin pleaded innocent to 12 charges of murder, torture and persecution of Bosnian Muslims and Croats in 1992. Zupljanin was charged with war crimes for allegedly overseeing Serb-run prison camps where thousands of Muslims and Croats were killed during the 1992-95 war in Bosnia.