The Minneapolis police officer who shot and killed Australian woman Justine Damond is in custody charged with her murder.

Mohamed Noor shot Ms Damond, a 40-year-old life coach on July 15, minutes after she called to report a possible sexual assault in the alley behind her home.

Mr Noor has not spoken publicly about the case and his lawyer, Thomas Plunkett, confirmed the officer turned himself in, but had no other immediate comment.

Jail documents said Mr Noor was being held on third-degree murder and second-degree manslaughter charges. Bail was set at US$500,000 ($650,000).

Ms Damond’s death cost the job of the Minneapolis police chief and forced major revisions to the department’s policy on body cameras.

Hennepin County Attorney Mike Freeman outlined the case against Mr Noor in a media conference on Wednesday morning (AEDT).

“We have a second-by-second understanding of what happened,” Mr Freeman said.

“In the short time between when Ms Damond Ruszczyk approached the squad car and the time that officer Noor fired the fatal shot, there is no evidence that officer Noor encountered a threat, appreciated a threat, investigated a threat or confirmed a threat that justified his decision to use deadly force.

“Instead officer Noor intentionally and recklessly fired his handgun from the passenger seat in disregard for human life.”

A policeman who was with Mr Noor at the time of the shooting, Matthew Harrity, told investigators that he was startled by a loud noise right before Ms Damond approached the driver’s side window of their police vehicle.

Mr Harrity, who was driving, said Mr Noor then leaned across and fired his weapon from the passenger seat.

Mr Harrity began CPR on Ms Damond, with Noor taking over afterward.

Ms Damond died of a gunshot wound to the abdomen before paramedics arrived.

The Ruszczyk family released a statement, describing the decision to charge Mr Noor as “one step toward justice for this iniquitous act”.

“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,” the statement released via the family’s lawyer Robert Bennett said.

“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,” it said.

The officers did not turn on their body cameras until after the shooting, and there was no video of the incident from the police car.

The lack of video was widely criticised and Ms Damond’s family members were among the many people who called for changes in procedure, including how often officers are required to turn on their cameras.

The shooting also prompted questions about the training of Mr Noor, a two-year veteran and Somali-American whose arrival on the force had been celebrated by city leaders and Minnesota’s large Somali community.

Mr Noor, 32, had trained in business and economics and worked in property management before becoming an officer.

-with AAP