A police officer has been formally charged with murder over the shooting death of an unarmed, naked black man with mental health problems.

A prosecutor in DeKalb County, Georgia, said that officer Robert Olsen was charged with a total of six crimes over the death of 27-year-old Anthony Hill.

Mr Hill, a US Air Force veteran who suffered from bipolar disorder and post-traumatic stress disorder, was having a manic episode when he was shot to death in March 2014 in the car park outside his apartment building.

Robert Olsen has been charged with six counts, including murder (AP)

Mr Olsen had told investigators that Mr Hill had been approaching him in what he said was a hostile manner and failed to respond to commands to stop.

As it was, he was on Thursday charged with murder, aggravated assault, violating his oath of office and making a false statement.

“My job as a prosecutor is to seek justice,” Mr James told a news conference, according to Reuters.

Mr Hill was an Air Force veteran (YouTube)

“That's what we do in every case, and that’s what we did in this case.”

Mr James said a warrant was issued for Mr Olsen’s arrest and that he expected him to be taken into custody soon. Mr Olsen’s lawyer, has yet to comment on the charges.

Protesters in Atlanta braved frigid nights and camped out in front of the courthouse this week, demanding justice for Mr Hill.

The incident was one of many that have sparked outcry across the US and led to allegations that some police officers discrimate agaisnt black and majority suspects.