The bones were found in a wooded area near the Five Sisters Business Park at West Calder by a dog-walker, who alerted police last Thursday.
A cordon was set up so that officers could search and examine the area.
Police today confirmed that the remains belonged to 53-year-old Martin Hamilton.
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Hamilton - who was known as the Blackhill butcher - had been freed from prison last September then broke his parole by disappearing.
His family has been informed and a post mortem examination will take place early next week.
The death is being treated as unexplained and a report will be sent to the Procurator Fiscal.
Detective Superintendent Kenny Graham said: “My condolences go out to the family of Martin Hamilton, who have had to receive such devastating news so close to Christmas. A team of officers is dedicated to this inquiry, so we can seek to give them answers as quickly as possible.
“We are continuing to conduct examinations with various scientific experts to establish exactly when and how Mr Hamilton died, and to ensure any evidence available can be captured from the scene and from the remains themselves.
“Work will be ongoing at the site near West Calder for several more days while we complete further searches and specialists carry out their work, so the area will stay closed off and the B7105 will also remain closed.”