Former Bosnian Serb army chief Ratko Mladic has been flown to the Netherlands, where he is to be tried at a UN war crimes tribunal in The Hague.
He was put on a plane in Belgrade shortly after a Serbian court rejected an appeal against his extradition.
Gen Mladic faces genocide charges over atrocities committed during the Bosnian conflict in the 1990s.
His lawyer had argued he was too ill to be tried. But Serbian doctors said he was fit enough to be extradited.
The 69-year-old was seized last Thursday in Lazarevo village, north of Belgrade, having been on the run for 16 years.
On Tuesday, a Belgrade court ruled that Gen Mladic was fit enough to be handed over to the UN's International Criminal Tribunal for the former Yugoslavia (ICTY) in The Hague.
Serbian Justice Minister Snezana Malovic later announced she had signed the extradition papers and that Gen Mladic was already on the plane.
The BBC's Mark Lowen in Belgrade says Gen Mladic's departure was even faster than most had predicted.
It seems the Serbian government acted to preempt any protests by his supporters by not making any announcement about the extradition until he was gone, our correspondent adds.
Candle and flowers
The Serbian government jet touched down at Rotterdam The Hague Airport at about 1945 local time (1745 GMT). It taxied from the runway into a hangar, whose doors were quickly closed.
Gen Mladic was then taken to the detention facility of the ICTY.
He is now due to receive a full medical examination, before appearing in court in the coming days.
He is accused of crimes against humanity, including the 1995 Srebrenica massacre of at least 7,500 Muslim men and boys.
Earlier on Tuesday, Gen Mladic had been allowed to visit the grave of his daughter Ana, albeit under heavy security.
Ana Mladic committed suicide in 1994 aged 23, reportedly shooting herself with her father's favourite pistol after she read about his alleged crimes in a magazine.
During the 20-minute visit to her grave, Gen Mladic lit a candle and left a small white bouquet of flowers with a red rose in the middle, said Serbia's deputy war crimes prosecutor, Bruno Vekaric.
Gen Mladic's arrest is considered crucial to Serbia's bid to join the European Union.
His son Darko Mladic said his father had told him he was not responsible for the killings in Srebrenica, committed after Bosnian Serb troops overran the town in July 1995.
Following the arrest of former Bosnian Serb leader Radovan Karadzic in 2008, Gen Mladic became the most prominent Bosnian war crimes suspect still at large.
He was indicted by the UN war crimes tribunal in The Hague in 1995 for genocide over Srebrenica - the worst single atrocity in Europe since World War II - and other alleged crimes.
Having lived freely in the Serbian capital, Belgrade, he disappeared after the arrest of former Yugoslav President Slobodan Milosevic in 2001.
Gen Mladic is still considered a war hero by many Serbs. On Tuesday thousands of people rallied in his support in Banja Luka, the capital of the Bosnian Serb entity, Republika Srpska.
"General Ratko Mladic is our brave son who led Republika Srpska's army and us soldiers to defend it," Bosnian Serb veteran Branislav Predojevic told AFP news agency.
On Sunday, thousands of people rallied in Belgrade against his arrest, condemning the pro-Western government of President Boris Tadic for arresting him.