"A dark chapter in European history can now be closed! And we can look at much brighter EU prospects for all of the Western Balkans," Bildt wrote on his Twitter account following reports of Mladic's arrest on Thursday.
Mladic, considered by many to be Europe's most wanted war crimes fugitive, is wanted for genocide in connection with the 1995 killing of some 8,000 Bosnian Muslims in Srebrenica and other crimes committed by troops under his command during Bosnia's 1992-95 war.
His arrest was announced on Thursday by Serbian president Boris Tadic, who added that Mladic's extradition to the UN war crimes tribunal in the Hague was already underway.
"My hope is that today's news will open up the possibility for Serbia to receive EU-candidate status toward the end of the year," Bildt wrote later on his blog.
"This is a good day for Europe."
Bildt, who served as a mediator in the conflict as a European Union Special Envoy and co-chaired the 1995 Dayton Peace Conference which brought an end to the hostilities, had extensive involvement with the Balkans following the dissolution of Yugoslavia in the early 1990s.
After the 1995 peace agreement, Bildt returned to Sarajevo to serve as the UN High Representative for Bosnia and Herzegovina until 1997, later assuming the post United Nations Secretary-General's Special Envoy for the Balkans between 1999 and 2001.
Bildt said he expects to be called to testify during the expected war crimes trial of Mladic at the International Criminal Tribunal for the former Yugoslavia (ICTY) to "tell what I know about what happened in the tragic summer of 1995".
"My meeting then with Mladic and others are described in the book 'Peace Journey', but since then various trials at the ICTY have given us a much deeper picture of what actually happened," Bildt wrote on his blog.
According to Bildt, the trial of Mladic will be "the last big war crimes trial following the Balkan wars" and that Mladic's arrest would also help Croatia's EU membership negotiations reach a successful conclusion "in the near future".
"Then the powers of European integration and forgiveness can finally begin to dominate that part of Europe which for a long and brutal and horrendous decade was torn apart by nationalist conflicts," wrote Bildt.