Colin MacDonald was jailed in 2014 for a campaign of abuse against three schoolgirls.
The 48-year-old served three-quarters of his jail-term before applying for early release.
He was reported missing last week, sparking a major search operation.
Detectives leading the hunt confirmed a man’s body was recovered at the weekend at Perth’s Kinnoull Hill.
Although the body has yet to be formally identified, MacDonald’s family has been informed.
Relatives were too upset to speak on Monday.
MacDonald was just 11-years-old when he targeted his first victim and spent the next six years preying on her.
The High Court in Edinburgh heard that he raped and sexually abused the youngster – who was just 10 when the attacks began – at locations in Inverness and Lochaber.
He also sexually assaulted a second girl in the early 1980s at an address in Fort William. She was just nine at the time.
And between the late 1980s and early 1990s, MacDonald repeatedly abused a third girl at an address in the Oban area.
Sentencing MacDonald in October 2014, Judge Lord Jones said he had no option but to send him to prison.
MacDonald had protested his innocence, claiming his victims had made up stories about him.
A Scottish Prison Service spokeswoman confirmed MacDonald had been eligible for early release after serving two-thirds of his sentence.
He was reported missing on Monday, April 23.
A helicopter was scrambled to search around the Kinnoull Hill area, while dog handlers patrolled at ground level.
On Friday, Police Scotland released CCTV images showing MacDonald walking through High Street and crossing Queen’s Bridge.
The images, captured at 2pm on April 23, were his last known sightings.
Chief Inspector Ian Scott, local area commander for the city, said on Friday that there was growing concern about MacDonald’s safety.
He said officers were in touch with his family who were “understandably upset and very concerned.”
Residents were urged to check their outhouses, sheds, garages and gardens in case MacDonald had been sleeping rough in the area.
