Keith Hall denied murdering Rachel Wilson, 19, in 2002 but admitted her manslaughter at Teesside Crown Court.
The CPS declined to pursue the murder charge as it would be “very difficult” to prove intent, the judge said.
The 62-year-old, of Middlesbrough, also admitted living off prostitution, in that he took money made by his victim. He will be sentenced on 29 June.
The long-time drug addict, from Lambton Road in Grove Hill, also admitted perverting the course of justice and now medical reports indicating his life expectancy will be 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.”
The Crown Prosecution Service explained to Ms Wilson’s family, who were in court, that it accepted a plea to the lesser charge of manslaughter because 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 multiple police appeals until June 2012 when her remains were found in a shallow grave on farmland near Coulby Newham.
The perverting the course of justice charge related to Hall trying to get a witness to change a police statement about a comment in which he incriminated himself over Ms Wilson’s death.
No details were given in court about how she died.
Speaking after the hearing, Temp Det Supt Paula Dewell from Cleveland Police’s Historical Investigation Unit said: “Keith Hall knows what he did to Rachel.
“He has let her mother and family go through turmoil for the last 19 years.
“I am pleased that we have been able to give justice to Rachel and resolve some unanswered questions for the family.”