Friday's bail allows the release of Muhamed Sacirbey, who also served as Bosnia's foreign minister, but requires that he be subjected to home detention and electronic monitoring.
US Magistrate Judge Frank Maas also ordered that Sacirbey post a $5 million personal bond and surrender any passports before being released.
The US government may appeal the bail order.
Although Maas previously denied bail to Sacirbey, he reconsidered after an official from the Federation of Bosnia and Herzegovina said he supported the former ambassador's release until a final extradition ruling is made.
Sacirbey, born in Sarajevo in 1956 and a naturalised US citizen, was arrested at his home in the New York borough of Staten Island in March 2003.
He is accused by Bosnia and Herzegovina of embezzling the funds while he was its UN ambassador in 2000. The charges carry a minimum term of three years in prison.
Sacirbey insists the charges are without merit.
He was first appointed as Bosnia's ambassador to the United Nations in 1992. He later served as Bosnia's foreign minister, before doing a second UN stint that ended in 2001.
A judge in Sarajevo issued a warrant for his arrest in 2001, charging that he stole about $2.5 million from accounts for the Investment Fund Ministry and UN mission.
The warrant says the funds were transferred to his private bank accounts while he was foreign minister.