Sarajevo was heavily shelled by Bosnian Serb forces and thousands killed during a siege of the city that lasted almost four years.
Haris Silajdzic, the Bosnian president, said news of Karadzic's arrest would provide "at least some satisfaction for the families of victims."
"Justice cannot be fully met without Karadzic's and Mladic's arrest"
But he cautioned that Karadzic's wartime commander, General Ratko Mladic, who was also indicted in 1995 for genocide and crimes against humanity, still remains at large.
"Justice cannot be fully met without Karadzic's and Mladic's arrest," he said, adding that "their project of ethnic cleansing unfortunately still lives on in Bosnia-Herzegovina."
In The Hague news of the arrest was welcomed in by the chief prosecutor of the UN tribunal for the former Yugoslavia, who said it marked an "important day for international justice".
"This is a very important day for the victims who have waited for this arrest for over a decade," Serge Brammertz said.
"It clearly demonstrates that nobody is beyond the reach of the law and that sooner or later all fugitives will be brought to justice."
Karadzic topped the tribunal's most-wanted list for more than a decade, allegedly resorting to elaborate disguises to evade capture.
Karadzic faces 11 war crimes charges including genocide, murder and inhumane acts committed during Bosnian war, among them leading the massacre of 8,000 Muslims in Srebrenica in 1995.
"The arrest of Radovan Karadzic is confirmation that every criminal will eventually face justice," said Munira Subasic, head of a Srebrenica widow's association.
"Ending impunity is an essential element for achieving sustainable peace and justice in the region"
UN secretary general
"I hope that people who had to keep quiet because of Karadzic will start revealing the locations of mass graves and let us find the truth about our beloved ones," she said.
At the United Nations in New York, Ban Ki-moon, the UN secretary general, welcomed what he said was "a historic moment for the victims" of the Bosnian war who he said had waited 13 years to see Karadzic brought to justice.
"Ending impunity is an essential element for achieving sustainable peace and justice in the region," Ban said.
"While this is an important milestone, the work of the International Tribunal will not be complete until all fugitives have been arrested and tried."
Since the end of the war, Bosnia has been divided into a republic run by Bosnia's Christian Orthodox Serbs and a federation between Muslim Bosnians and Catholic Croats.
In the Serbian part, reaction was said to be muted with no comment from officials.
Local TV showed a reporter stopping several cab drivers in the northern city of Banja Luka – one driver said Karadzic's arrest was a "tragedy".
In the Serbian capital, Belgrade, news of his arrest was met with an angry reaction from nationalists who consider Karadzic a war hero.
"He did not surrender, that is not his style," his brother Luka Karadzic said outside the court where he was being held.
Dozens of Karadzic supporters gathered near the building chanted "Karadzic Hero!" and "Tadic Traitor!", referring to the Serbian president, Boris Tadic.