Hunters discovered the remains of the 66 year-old on Sunday morning and alerted police.
The retired librarian and former Leicester councillor was last seen on June 9th when he set off from a hostel in Huercal-Overa to walk to nearby Albox.
Described as an experience hiker, Oldman was attempting to walk a 2,250 Km trek from London to Gibraltar, a trip he was making in stages.
His family became concerned after he failed to phone home and missed his return flight back to London on June 13th.
Friends and family launched appeals on social media and last month travelled to Almeria to walk the 20km route between the towns where he went missing.
His body was discovered by a group of hunters who called the police. A post-mortem is due to be carried out on Monday to determine the cause of death.