Serbian President Boris Tadic said the process to extradite the former Bosnian Serb army chief to the war crimes tribunal in The Hague was under way.
Gen Mladic is accused over the massacre of at least 7,500 Bosnian Muslim men and boys at Srebrenica in 1995.
He was the most prominent Bosnian war crimes suspect at large since the arrest of Radovan Karadzic in 2008.
The detention, the Serbian leader said, closed one chapter in Serbian history, bringing the country and the region closer to reconciliation.
It also opened the doors to membership of the European Union, he added.
Serbian media initially reported that Mr Mladic was already on his way to the Hague, but Serbian prosecutors later said the procedure to extradite him might take a week.
It is hard to overstate the importance of this arrest here in Serbia. Many people feel the destiny of their country was held hostage by Ratko Mladic. Their hopes of joining the EU were ruled out by Brussels while Mladic was at large.
I asked President Tadic if it was a coincidence that he was arrested while the EU was considering Serbia's bid to join the bloc. He said the country had never calculated its search for Mladic - it was always determined to catch him.
There is still an ultra-nationalist fringe here who see Mladic as a hero - they say he only ever defended Serb interests. But the new, emerging generation in Serbia seem to be tired of the past and its wars - they want to leave that behind and move forward to the future.
A spokeswoman for families of Srebrenica victims, Hajra Catic, told AFP news agency: "After 16 years of waiting, for us, the victims' families, this is a relief."
UN war crimes chief prosecutor Serge Brammertz welcomed the arrest, saying: "Today's events show that people responsible for grave violations of international humanitarian law can no longer count on impunity."
In other reaction:
US deputy national security adviser Ben Rhodes said the US was "delighted"
UK Defence Secretary Liam Fox said it was a chance for Serbians to "close a very unhappy chapter in their history"
Nato chief Anders Fogh Rasmussen said the arrest finally offered "a chance for justice to be done"
Swedish Foreign Minister Carl Bildt said Serbia's EU prospects were "now brighter than ever"
1995: Gen Mladic indicted by the International Criminal Tribunal for the Former Yugoslavia, accused of genocide, crimes against humanity, and war crimes
October 2000: Former Yugoslav President Slobodan Milosevic ousted and arrested the following year; Gen Mladic, believed to be living in Serbia, disappears from view
April 2005: Serbian Foreign Minister Vuk Draskovic says Serbian security agents knew Gen Mladic's whereabouts; the intelligence agency describes the allegations as "ridiculous"
February 2006: Chief UN prosecutor demands Serbia step up the hunt for Gen Mladic and says the failure to arrest him will harm Serbia's EU membership chances
July 2008: Gen Mladic's mentor, Bosnian Serb former political leader Radovan Karadzic, captured
October 2010: Serbia offers 10m euros (£8.7m) for information leading to Gen Mladic's capture and arrest
Ratko Mladic's very personal war
UK hails 'historic' Mladic arrest
Gen Mladic was said by Serbian media to have been arrested in Vojvodina, a northern province of Serbia, in the early hours of Thursday.
President Tadic would only confirm he had been arrested "on Serbian soil", adding that details of the arrest would be released once an investigation had been completed.
Gen Mladic had reportedly been using the assumed name Milorad Komodic.
Serbian security sources told AFP that three special units had descended on a house in the village of Lazarevo, about 80km (50 miles) north of Belgrade.
The house was owned by a relative of Gen Mladic and had been under surveillance for the past two weeks, one of the sources added.
Gen Mladic was indicted by the UN war crimes tribunal in The Hague in 1995 for genocide over the killings that July at Srebrenica - the worst single atrocity in Europe since World War II - and other crimes.
Having lived freely in the Serbian capital, Belgrade, he disappeared after the arrest of former Yugoslav President Slobodan Milosevic in 2001.
Speculation mounted that Gen Mladic would eventually be arrested when Mr Karadzic was captured in Belgrade in July 2008.
Larry Hollingworth, a logistics officer with the UN refugee agency who regularly met Gen Mladic during the Bosnian war, said he was "absolutely delighted" by news of the arrest.
"He was a very, very imposing figure and managed to frighten a lot of people - certainly those who worked for him," he told BBC Radio 4.
'Unimaginable horrors'
Just before news of Thursday's arrest, Mr Brammertz had accused Serbia of failing to do enough to find Gen Mladic.
"Until now efforts by Serbia to detain fugitives have not been sufficient," he said in a report sent to the UN Security Council.
President Tadic rejected criticism that Serbia had only taken action following international pressure.
"It is crystal clear that we did not calculate when we had to arrest Ratko Mladic," he told the news conference on Thursday.
Srebrenica falls to Bosnian Serbs - archive BBC report from 1995
"We have been co-operating with the Hague Tribunal fully from the beginning of the mandate of this government."
Speaking after the arrest, Mr Brammertz said UN prosecutors recognised the work done by the Serbian authorities and thanked them for "meeting their obligations towards the tribunal and towards justice".
"With the news of the arrest, we think first and foremost of the victims of the crimes committed during the conflicts in the former Yugoslavia," he added.
"These victims have endured unimaginable horrors - including the genocide in Srebrenica - and redress for their suffering is long overdue," the war crimes prosecutor said.