The bureau initially said witnesses described Brooks being shot "in the struggle over the Taser".
But, after obtaining Wendy's surveillance video, it revised its account, saying it "was based on the officer's body cam which was knocked off during the physical struggle, preventing the capture of the entire shooting incident".
"During the chase, Mr Brooks turned and pointed the Taser at the officer," the bureau said, adding that "the officer fired his weapon, striking Brooks."
POLICE CHIEF RESIGNS, DEADLY FORCE 'NOT JUSTIFIED'
The release of the surveillance footage follows Atlanta Mayor Keisha Lance Bottoms announcement that police chief Erika Shields had resigned over the fatal shooting.
Amid mounting rage over the killing, Bottoms called for the immediate termination of the officer involved.
"While there may be debate as to whether this was an appropriate use of deadly force, I firmly believe that there is a clear distinction between what you can do and what you should do," Bottoms told reporters.
"I do not believe that this was a justified use of deadly force.
"What has become abundantly clear over the last couple of weeks in Atlanta is that, while we have a police force full of men and women who work alongside our communities with honour, respect and dignity, there has been a disconnect with what our expectations are and should be as it relates to interactions with our officers and the communities in which they are entrusted to protect."
Atlanta Police asked the Georgia Bureau of Investigation to investigate the incident, which comes amid the Black Lives Matter protests over George Floyd's death.
"The killing of #RayshardBrooks in Atlanta last night demands we severely restrict the use of deadly force," former Democratic candidate Stacey Abrams tweeted.
"Yes, investigations must be called for – but so too should accountability. Sleeping in a drive-thru must not end in death."
"Why would you shoot a drunk man running away from you with deadly force? #RayshardBrooks should be alive today – he fell asleep at a drive-thru and is now dead as a result of police action. This has to end," political commentator Andrew Yang tweeted.
"Struggling with police is not punishable by death. Grabbing a taser to stop from being tased isn't punishable by death. Running away from police on foot, unarmed isn't punishable by death. But the Atlanta police murdered #RayshardBrooks," another user wrote.
PROTESTERS CROWD ATLANTA AFTER SHOOTING
Atlanta is among US cities where large crowds have taken to the streets to protest the May 25 death of George Floyd in Minneapolis.
A crowd of demonstrators also gathered outside the Atlanta restaurant where Brooks was shot.
Gerald Griggs, a lawyer, estimated there were 150 people protesting with him at the scene.
"The people are upset," Griggs said. "They want to know why their dear brother Rayshard Brooks was shot and killed when he was merely asleep on the passenger side and not doing anything."
Even though Brooks struggled with officers, Griggs said, "they could have used non-lethal force to take him down."
After Brooks failed a field sobriety test, officers attempted to place him into custody but a struggle ensued, leading the officer to deploy a Taser.
"Ultimately, when the officer used a Taser, it was ineffective for the suspect," Atlanta deputy police chief Timothy Peek said. "It did not stop the aggression of the fight. And so the suspect was able to take the officer's Taser from him."
Peek said a second officer also attempted to use a Taser "but it didn't work against the suspect as well".
Brooks died in a local hospital after surgery.
One officer was treated for an injury and discharged from the hospital.
Fulton County District Attorney Paul Howard said his office had already had already launched an "intense, independent investigation of the incident".
