Lord Justice Laws, who announced Ganic's bail, said that a sum of $450,000 had been provided as security by a "well-wisher" who was, the court understood, "a lady of substantial means".
The judge also required a surety of $38,000 which was provided by the vice-chancellor of the University of Buckingham, a colleague of Ganic.
The former Bosnian leader, who is is likely to be released from London's Wandsworth prison later Thursday, was not present for the verdict.
But his son Emir and daughter Emina, who attended the hearing, welcomed the outcome.
"We are very happy with the outcome, it has been very emotional.
"This is just the first step. My father is an academic who has never spent a day in prison before," Emir Ganic said.
Serbia has said Ganic and a number of other people are suspected of war crimes, and blames them for the 1992 attack on a Yugoslav convoy in Sarajevo, when more than 40 soldiers were killed.
The attack took place at the start of the 1992-95 war which erupted when Bosnia declared independence from the former Yugoslavia.
But Ganic's lawyers say moves to make him face trial in Serbia are politically-motivated and that his arrest was illegal.
Bosnia has argued that the allegations against Ganic are designed to minimise Serbia's blame for the 1992-5 war, which tore the Balkans apart.