The identification was confirmed by the South African Police Service (SAPS) in a statement on Monday afternoon.
It brought an agonising search for Moselakgomo to an end after she went missing last week while out for a run.
Her identification came as police investigate the deaths of women in the Kempton Park area and confirmed the discovery of a fifth woman’s body on Monday.
“We extend our deepest sympathies to the family and loved ones of Elizabeth during this extremely painful time. The loss of a loved one under such circumstances is devastating, and we assure the family that the SAPS will do everything within its powers to establish exactly what happened to Elizabeth and to ensure that those responsible are held accountable,” said Acting National Commissioner of SAPS Lieutenant General Puleng Dimpane.
The body found on Saturday was initially treated as unidentified while Moselakgomo’s family waited for the formal identification process to be completed.
The development was followed by the discovery of another woman’s body on Monday, bringing the number of bodies found in the area to five.
The latest discovery has intensified concerns among residents and members of the local running community, particularly over similarities between some of the cases.
SAPS said a multidisciplinary team comprising detectives and specialised policing resources had been directed to intensify the investigations.
Police have acknowledged similarities in some of the killings but have not confirmed that a serial killer is responsible.
SAPS said the similarities were being investigated and that it would be premature to conclude that the cases were connected until evidence established a link.
“We will not rest until we have established the truth. Where there is evidence linking individuals to these crimes, we will pursue them relentlessly and ensure that they face the full might of the law,” Dimpane said.
The developments have left the Kempton Park community increasingly concerned about the safety of women, particularly those who exercise or travel alone in the area.
One suspect has already been arrested in connection with the discovery of the first body in July and remains in custody, according to SAPS.
