The 53-year-old's body was discovered by a dog walker near West Calder on 17 December.
Police said a post mortem examination revealed he had suffered serious injuries which are believed to have led to his death.
Hamilton, from Glasgow, was previously one of Scotland's most wanted men.
He was released from prison in September 2014 but was sought by police in April for breaching the terms of his licence.
At the time, police described him as "potentially dangerous".
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.
Police officers and scientific experts were continuing to work at the scene where his remains were discovered.
A spokesman said specially trained officers were providing support to Martin Hamilton's family.
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.
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.
The death of Martin Hamilton whose remains were found in West Lothian earlier this month is being treated as murder.