Tracy Gabriel, 40, and Keith Taylor, 43, were found dead at Donside Court in the Tillydrone area last July.
Hugh Gallacher then fell to his death shortly after police arrived.
The Crown Office said no further investigation in the case was now required.
It is understood the 56-year-old had stabbed Ms Gabriel and Mr Taylor to death.
The Crown Office said in a statement: "The Police Investigations and Review Commissioner (PIRC) has submitted a report to COPFS concerning the circumstances surrounding the death of a 56-year-old man following a disturbance in which two men and a woman died at a flat in Donside Court, Aberdeen, on Tuesday 19 July.
"After careful consideration of the facts and circumstances of the case, the Procurator Fiscal concluded that no further investigation is required.
"We have contacted families of the deceased and offered a meeting to discuss the matter."
A spokeswoman for the PIRC said their report was submitted to the Crown in November and they could not comment on the contents, adding it was up to the Crown to decide what action to take.
Ms Gabriel, who was originally from Huntly, was reported to have been a mother of four children.
Police officers have been cleared of any wrongdoing following an investigation into the circumstances surrounding the deaths of three people in an Aberdeen tower block.