It's "obviously highly important. We can start to close a tragic chapter in the history of Europe," Carl Bildt told Reuters. "The European prospects of Serbia are now brighter than ever."
Serbia applied to join the EU in 2009. The European Commission is due to decide in October whether to grant Serbia candidate status and recommend that the EU launches accession talks with Belgrade.
Arresting Mladic will likely go a long way in convincing Brussels that Serbia is ready to start negotiations.
Belgrade's full cooperation with the International Criminal Court for the Former Yugoslavia, which has indicted Mladic on genocide charges, is a key requirement for Serbia.
However, the Commission may delay a positive recommendation in October, if that last wanted war crimes suspect Goran Hadzic is not arrested by then.
"I warmly congratulate President (Boris) Tadic," Bildt said. "I knew his determination to achieve this, and know how hard he worked for it."