Permission to film had been withdrawn last week, with the government citing incomplete paperwork.
"I can now start preparations for the shooting, which I had to stop last week," Edin Sarkic, an executive with the movie's Sarajevo-based Scout Film, said.
"It's a big thing for Bosnia that such a mega, mega star is coming to Sarajevo."
The Oscar-winning actress is shooting the film in Budapest. Her production company said it was a love story between a Serbian man and a Bosnian Muslim woman who meet on the eve of the Bosnian 1992-95 war, which killed 100,000 people.
The outgoing culture minister of Bosnia's Muslim-Croat federation, Gavrilo Grahovac, has now approved the filming after being given a script and a list of locations, his ministry said.
Last Wednesday, Grahovac had canceled a permit.
That decision, made after he met an association of female victims from the Bosnian war who had objected to what they said were details of the plot, caused a public outcry in Bosnia.
Bakira Hasecic, president of the Women Victims of War association, had urged Bosnian authorities to ban the shooting of the film, saying the script distorted the truth about female war victims.
Jolie has said the film would not meddle in politics and has tried to reassure the victims about its content.
"There are many twists in the plot that address the sensitive nature of the relationship between the main characters and that will be revealed once the film is released," she said last week. "My hope is that people will hold judgment until they have seen the film."
Bosnian filming should start in November, Sarkic said.
