Keith Hall, 62, denied murdering Rachel Wilson, 19, in 2002 but admitted her manslaughter before his trial was due to start at Teesside Crown Court.
The defendant, of Lambton Road, Grove Hill, Middlesbrough, also admitted perverting the course of justice and living off prostitution, in that he took money made by his victim.
The long-time drug addict will be sentenced on June 29 after medical reports indicating his life expectancy are produced.
Mrs Justice Lambert told Hall: “Whatever the content of that medical report, it is very likely I will be imposing a significant custodial sentence upon you.”
Ms Wilson’s family, who were in court, understood why the Crown Prosecution Service accepted the plea to the lesser charge of manslaughter after it was explained to them that a murder charge would require them to prove Hall’s intent, the court heard.
Mrs Justice Lambert said: “I quite understand why the family have been sanguine and accepted the plea. It would have been very difficult to prove the intent. I understand the advice and the family’s acceptance of that.”
Ms Wilson was last seen in May 2002 and her disappearance was the subject of many police appeals until June 2012 when her remains were found in a shallow grave on farmland near Coulby Newham in North Yorkshire.
Hall was under suspicion and investigated for years while Cleveland Police built their case against him.
The perverting the course of justice charge related to him trying to get a witness to change a statement to police about a comment in which Hall incriminated himself in relation to Ms Wilson’s death.
No details were given in court about how she died.
Hall was remanded in custody.
The Home Office funded Cleveland Police’s Historical Investigation Unit special grant to reinvestigate the the cases of three missing women – Ms Wilson, Donna Keogh and Vicky Glass.
Temporary Detective Superintendent Paula Dewell from the unit said: “Rachel’s case proves that Cleveland Police will not give up in the fight for justice for victims and their families. Everyone who has worked tirelessly on Rachel’s case did so with the aim of ensuring that the person responsible for her death is convicted and put behind bars.
“Keith Hall knows what he did to Rachel. He has let her mother and family go through turmoil for the last 19 years. He hid her body in 2002 and left them not knowing where she was or what had happened.
“By chance, Rachel’s body was found in 2012, but her family were still facing the prospect of not seeing the person responsible for her death brought to justice. I am pleased that we have been able to give justice to Rachel and resolve some unanswered questions for the family.
“I know that they will never be able to move on from Rachel’s death, but I hope that today’s result will provide them with some comfort. I am so proud of the team for their work, they have achieved more than others who have gone before, and will go on with the aim of seeking justice for Donna Keogh and Vicky Glass.”