"The transfer of Milosevic to The Hague is an unequivocal message to those persons who brought such a tragedy and brutality to the Balkans that they will be held accountable for their crimes," Mr Bush said in a statement issued by the White House.
US President George Bush applauded the extradition, saying the transfer signalled "the commitment of the new leadership in Belgrade to turn Yugoslavia away from its tragic past and toward a brighter future."
"The transfer of Milosevic to The Hague is an unequivocal message to those persons who brought such a tragedy and brutality to the Balkans that they will be held accountable for their crimes," Mr Bush said in a statement issued by the White House.
But members of the Russian parliament said extradition would represent an end to Yugoslavia and its statehood.
Moscow has yet to react officially to the transfer of Mr Milosevic to The Hague. But the speaker of the Russian parliament's upper house condemned western governments for bullying Belgrade on Thursday.
Cash pledge
Meanwhile, the European Commission said Mr Milosevic's transfer would help Belgrade raise cash at the international donor conference on Friday.
Donors preparing to attend the conference in Brussels, which will be chaired jointly by the European Commission and the World Bank, had demanded Mr Milosevic's transfer.
"This is very good news and will certainly have a positive effect on donors' attitudes. It will help ensure that what is pledged is swiftly followed up," Commission spokesman Gunnar Wiegand told Reuters.
U.N. Secretary-General Kofi Annan said the transfer was a "victory for accountability over impunity."
"To the many victims of the Balkan wars of the past decade, I hope this day will bring some measure of comfort, some sense that even the most powerful leader can be brought to justice and face the consequences of his actions," he said.
'Wise and courageous'
Nato Secretary-General Lord Robertson praised Mr Milosevic's handover to the tribunal and congratulated Belgrade authorities for their "wise and courageous decision".
UK Prime Minister Tony Blair, who is holding talks in Northern Ireland, also hailed the handover as "indeed good news".
French President Jacques Chirac commended the Belgrade authorities for what he called a "major contribution to the affirmation of law and justice in the world".
He added that "Everybody will know from now on that one cannot flout with impunity the essential values of human dignity."
And in Vienna the Austrian Foreign Minister Benita Ferrero-Waldner welcomed reports of the extradition.
"This shows that, slowly but surely, democracy is taking hold in the Balkans and that democratic rules, according to which war criminals must be handed over, are being respected," the minister was quoted as saying.
Former EU special envoy to Yugoslavia Lord Owen told the BBC it was in the overall interests of the Serbian people that Mr Milosevic should be put on trial.
He said the former president's absence from The Hague tribunal had deprived them of urgently needed international aid.