Murderer Aaron Campbell was convicted at the High Court in Glasgow in March where a jury found him guilty unanimously following a nine-day trial.
The 16-year-old abducted, raped and murdered the youngster and been locked up for at least 27 years.
Alesha’s body was found in woods on the Isle of Bute on July 2 last year, hours after she was reported missing from the house her father shared with his parents and partner on the island.
The girl was days into her summer holiday with father Robert MacPhail, 26, and grandparents Angela King and Calum MacPhail when she was snatched by Campbell, who tried to blame her father’s girlfriend Toni McLachlan, 18, for the crime.
In early April it was reported that Campbell would be appealing his life sentence for the horrific killing.
It is understood that appeal has now been granted, with a three-judge hearing set to take place in Edinburgh on 7 August.