Martin Hamilton's body was discovered by a dog walker in woodland near West Calder on 17 December.
The 53-year-old, who was from Glasgow, was released from prison in September 2014 but was sought by police in April for breaching the terms of his licence.
Police described him at the time as "potentially dangerous". His death was being treated as unexplained.
Hamilton was nicknamed the Blackhill Butcher, after the Glasgow housing estate from which he operated.
He had been on the police's most-wanted list before he was jailed in 2000 over a string of charges including drug dealing, torture, abduction and sodomy.
Hamilton was sentenced to a minimum of nine years in prison after being found guilty at the High Court in Inverness.
The case was moved 200 miles from Glasgow amid fears that witnesses could be intimidated. Hamilton had evaded justice on 12 previous occasions when witnesses were too terrified to testify.
In court, a sickening picture emerged of how Hamilton, also known as the Fat Controller, entrapped young men with offers of drugs.
Two young drug addicts were imprisoned in a Glasgow flat, stabbed through the cheek and had boiling water poured over them.
Another attack in Edinburgh included an attempt to cut off a victim's finger.
Passing sentence, judge Lord Kingarth said: "You showed yourself capable of taking sadistic pleasure in the infliction of pain and the inspiration of real terror over long periods. You pose a substantial danger to the public."
When Police Scotland issued an appeal to find Hamilton in April they said he may be dangerous and urged members of the public not to approach him. A further appeal was made in June.
In October, an appeal was made on the BBC's Crimewatch programme and the Crimestoppers charity also offered a reward of Â£2,000 for information leading to his arrest.
Det Supt Kenny Graham said the site near West Calder where the remains were found would stay closed off or several more days "whilst we complete further searches and specialists carry out their work".
The nearby B7105 will also remain closed.
Det Supt 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."

The group is consulting with 33 staff on plans to close its printing site near Cardiff Docks.
Trinity Mirror wants to print the Western Mail in Watford and the South Wales Echo in Oxford, it is understood.
The company said the consultation process was ongoing.
The group previously blamed "declining print volumes and the relocation of a number of titles within our print network" for the proposed closure of the print works, which is responsible for a number of Trinity Mirror newspapers as well as other publications.
Trinity Mirror also owns Wales on Sunday, which is already printed in Birmingham, as well as the South Wales Evening Post and the Daily Post.
Meanwhile, BBC Wales understands the company is in talks to sell its Media Wales building in Cardiff city centre.
The company plans to remain as a tenant when the deal is completed.
Media Wales moved into the six storey purpose-built office block on Park Street in 2008.
Staff cuts mean its sales and editorial teams now only occupy one floor, while accountancy firm Deloitte has taken some of the vacant space.
Trinity Mirror declined to comment on the proposed sale of its Media Wales headquarters.
Human remains found in West Lothian last week have been identified as one of Scotland's most wanted men.
[NEXT_CONCEPT]
Newspaper publisher Trinity Mirror plans to print some of its Welsh titles in London and Oxford when it closes its presses in Cardiff, BBC Wales has learned.