The woman, Becky Godden-Edwards, would have been 29 years old on Monday.
Detectives working on the case had scoured national databases in a bid to work out who was buried at Eastleach in Gloucestershire.
Taxi driver Christopher Halliwell, 47, from Swindon, has been charged with 22-year-old Miss O'Callaghan's murder.
Det Supt Steve Fulcher, of Wiltshire Police, said officers had developed a DNA profile from the bones that were recovered in the Cotswolds.
"As you will appreciate, Becky's family and loved ones are trying to come to terms with this devastating news and we are affording them all the comfort and sympathy we can at this time, helping them come to terms with their grief," he said.
Miss Godden-Edwards, who was from the Shaw area of Swindon, was reported to the national Missing People Helpline in 2007 by her family when they became concerned by the lack of contact from her, Mr Fulcher said.
He told a press conference: "Inquiries are continuing to establish the circumstances surrounding Becky's disappearance and subsequent death.
"Part of these inquiries will be to speak to Chris Halliwell and we will then make a decision on any appropriate steps to take."
The detective appealed to anyone who knew Miss Godden-Edwards from 2002 onwards to contact the police or Crimestoppers.
"What I'm interested in are Becky's movements, her friends, her lifestyle, any small information which will help me piece back together how she came to meet her death," he said.
"I will respect confidences where people ask for it."
BBC correspondent Jon Kay said it was understood that Miss Godden-Edwards had become "disconnected" from her family.
Her family are believed to have lost contact with her in 2003. They initially did not report her missing to the police and they thought she was living in the Bristol area.
In a statement, the Edwards family said: "The family is completely devastated by the news of Becky's death and at this time wish to be left alone to grieve for our beautiful daughter."
Police investigating the murder of Sian O'Callaghan have identified human remains found at a second site as a Swindon woman missing for eight years.