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.
Aaron Campbell was convicted at the High Court in Glasgow last month where a jury found him guilty unanimously following a nine-day trial.
Lord Matthews sentenced him to life imprisonment and ordered him to spend at least 27 years behind bars when he appeared at the court on Thursday.
Campbell could not be identified during the trial due to his age but following his conviction judge Lord Matthews lifted a ban on revealing his identity.
The teenager took Alesha from her bed as she slept and inflicted horrific injuries before dumping her body in nearby woodland.
Pathologist John Williams told the trial Alesha had 117 separate injuries, and a post-mortem examination indicated she had died from “significant and forceful pressure to her neck and face”.
Alesha 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.
Prosecutor Iain McSporran said he hoped the guilty verdict would remove any doubt that she could have been involved.
CCTV footage from Campbell’s mother’s own security system provided evidence which helped detectives catch the killer.
His mother had contacted police herself, hoping the footage would eliminate her son from the investigation.
Campbell was captured coming and going from his home several times in the early hours of July 2, removing items of clothing and retrieving a torch.
A psychological evaluation carried out on July 9 and 10 last year highlighted no issues to suggest he was not of sound mind when he murdered Alesha.
At a hearing after the trial ended it emerged the teenager had a history of self harm, anxiety and depression, and has been tested for attention deficit hyperactivity disorder.