"The court concludes ... there were acts of genocide committed by members of the Bosnian Serb army (in Srebrenica)," ICJ president Rosalyn Higgins was quoted as saying by Agence France-Presse (AFP).
More than 8,000 Muslim men and boys were massacred after Serb forces overran Srebrenica, then a United Nations "safe haven", in July 1995.
The massacre aimed to ensure there were no Muslims to fight back or reclaim Serb-occupied land or homes in the future.
The International Criminal Tribunal for the former Yugoslavia (ICTY), the UN's ad hoc war crimes court, has already ruled that the Srebrenica massacre was an act of genocide.
The court has also convicted two former Bosnian Serb military officers for aiding and abetting the slaughter.
Genocide was made an international crime under a 1948 treaty.
Proving genocide requires establishing intent to destroy a group, in whole or in part, as well as demonstrating that genocidal acts such as the Srebrenica massacre took place.
The binding ICJ ruling said that Serbia had violated international law by failing to act to prevent the Srebrenica genocide.
It stressed that Serbia "was making considerable military and financial support available to the (Bosnian Serb entity) Republika Srpska" during the Bosnian war.
Muslims and Croats accuse Belgrade of failing to own up to the crimes committed in the nationalist cause of a "Greater Serbia" in the 1990s, while Serbia argues that all parties to the conflict were guilty of atrocities.
Backed by the Yugoslav army, Bosnian Serbs attacked Bosnian Muslims and Croats, capturing two-thirds of Bosnia and besieging Sarajevo.
Serbia under then-president Slobodan Milosevic was the main backer of ethnic Serb forces in Bosnia.
Milosevic, seen as the architect of the ethnic cleansing campaign in Bosnia, died in UN custody last year before any verdict could be reached on the genocide and war crimes charges against him in the ICTY.
But the court judged that Serbia did not commit genocide and would not have to pay financial compensation.
"The court finds that Serbia has not committed genocide," Higgins said.
Bosnia has accused Serbia of masterminding the widespread "ethnic cleansing" of Bosnian Muslims and Croats during the 1992-1995 war.
At least 200,000 people were killed and thousands forced from their homes in the 1992-1995 war, triggered by the break-up of the former Yugoslavia.
Nearly 20,000 Muslim women were systematically raped during the war.
The ICJ's genocide ruling is the first to deal with disputes between states.
"Whatever the court may rule, Bosnia and Hercegovina vs Serbia and Montenegro is a historic case because there has been no previous ruling," Geraldine Mattioli, an expert with the Human Rights Watch group, told AFP.Güncelleme Tarihi: 20 Eylül 2018, 18:16