A Minneapolis police officer who shot and killed an unarmed Australian woman has been charged with third-degree murder and second-degree manslaughter.

Officer Mohamed Noor turned himself in on Tuesday after a warrant was issued for his arrest.

Noor was booked into Hennepin County jail on Tuesday morning and bail was set at $US500,000 ($A650,000).

"Such actions violate the criminal law," Hennepin County Attorney Mike Freeman told reporters at a press conference on Tuesday. Ms Damond's family is pleased justice may be served with the Minneapolis police officer being charged.

"We remain hopeful that a strong case will be presented by the prosecutor, backed by verified and detailed forensic evidence, and that this will lead to a conviction," Damond's fiance Don Damond and her Sydney-based father John Ruszczyk and other family members said in a joint statement. 

"No charges can bring our Justine back.

"However, justice demands accountability for those responsible for recklessly killing the fellow citizens they are sworn to protect, and today's actions reflect that."

Noor fatally shot 40-year-old Ms Damond as she approached his police car in an alley just before midnight on July 15.

Ms Damond was dressed in her pyjamas and earlier had called 911 to report the screams of a woman who could have been sexually assaulted in the alley behind her home.