The six-year-old, from Airdrie, was found dead on the Isle of Bute on Monday. She had been staying at her grandparents house in Port Bannatyne, near Rothesay, when she was reported missing.
The teenager, who was arrested yesterday, is expected to appear before Greenock Sheriff Court on Friday.
Alesha was a few days into a three-week summer break on the island in the Firth of Clyde, west of Glasgow.
Police Scotland said the boy charged remains in custody.
Detective Superintendent Stuart Houston said: “I’d like to take this opportunity to personally thank Alesha’s family who have shown incredible bravery through what has been an unimaginable ordeal during these past few days.
“I’d also like to thank local people for all their support and assistance during this major investigation on the island. The response to our appeals was significant both from those living here and the wider community of Scotland.
“The people of the Isle of Bute have rallied together since Alesha was first reported missing on Monday morning and I would stress that social media speculation relating to members of the community is both misleading and inaccurate.
“The family has also received considerable support from Alesha’s home town of Airdrie which was reflected in the memorial service held at her school.
“Officers and staff from across Police Scotland and the Scottish Police Authority have been involved in what has been a difficult and challenging investigation during which they have worked tirelessly to bring us to where we are today.
“As I have said previously, incidents such as this are extremely rare and while the police investigation will continue, I hope that today’s announcement brings some reassurance to everyone in the local community.
“It is understandable that recent events will have shocked communities across Scotland, no more so than on Bute and in Airdrie. Argyll and Bute and North Lanarkshire councils have services available for those who may have been affected.”