"He was a giant in modern global diplomacy. I will miss him. The United States will be poorer without Richard Holbrooke," Bildt wrote on his blog concerning the 69-year-old US special envoy to Afghanistan and Pakistan who died overnight.
Bildt worked closely with Holbrooke and others to broker the 1995 treaty that ended the Bosnian war, with the US diplomat receiving credit for hammering out a treaty that many privately thought would be impossible.
"I can still remember like yesterday the daily rollercoaster ride of diplomacy, disputes, hope and disappointment that we were thrown into together during those dramatic months," Bildt wrote, adding that Holbrooke's work on the treaty was "absolutely decisive."
Holbrooke, who was Obama's special US envoy in the current Afghan conflict, fell ill at work on Friday and was rushed to a Washington hospital, undergoing surgery for a torn aorta. He died Monday US officials said.
"Soldiers die in battle, but diplomats seldom do. Richard Holbrooke was I think an exception in this respect. He died in the middle of one of modern diplomacy's most difficult and most important battles," Bildt wrote in his long tribute.