Officers discovered the remains during a detailed search of a farm in Kirknewton this afternoon. They said enquiries were ongoing to establish the identity.
Alex Cameron, 67, was sent to prison in 2010 after being found guilty of developing a profitable drug empire from his West Lothian farm.
He was said to have gone missing on January 19 from his home in Newcraighall Road.
James Smith, 58, made a brief appearance in private at Livingston Sheriff Court on Tuesday charged with Mr Cameron’s murder.
He made no plea or declaration to charges of murder and attempting to defeat the ends of justice.
Smith, from Kirknewton, was remanded in custody and the case was committed for further examination.
He is expected to make his next appearance within a week.