Aaron Campbell, 17, was ordered to spend a minimum of 27 years behind bars for abducting and killing the schoolgirl during a holiday on the Isle of Bute last summer.
A court spokesman confirmed Campbell has been granted leave to appeal the life sentence handed down by Lord Matthews at the High Court in Glasgow in March.
A hearing date has been set for August 7 at the High Court in Edinburgh.
Campbell snatched Alesha from her bed as she slept at her grandparents' home in July last year.
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He inflicted horrific injuries on the child before dumping her body in nearby woodland.
A jury found him guilty unanimously following a nine-day trial, and he later admitted the crime to those assessing him.
Judge Lord Matthews described Campbell as "calculating and remorseless" before ordering him to spend life behind bars, and warning he may never be released.
The court heard that the teenager had said he was "quite satisfied by themurder."