The six-year-old died after going missing from her grandparents home on the Isle of Bute with a 16-year-old since being charged for her murder.
The teen is due to appear at Greenock Sheriff Court.
Speaking to the media, Detective Superintendent Stuart Houston praised their “incredible bravery” of the family as they dealt with the murder.
He also praised islanders for how they had responded since the incident in aiding police in their investigation.
DS Houston said: “I would like to thank local people for their support and assistance in this major investigation.
“The response to our appeals was significant from those 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.”
DS Houston thanked Alesha’s family and locals in her home town Airdrie including mum Georgina Lochrane, 23.
He said: “I’d like to thank Alesha’s family who have shown incredible bravery through an unimaginable ordeal in these past few days.
“The family has also received considerable support from Alesha’s home town, reflected in the memorial service at her school.
“Officers and staff from across Police Scotland and the Scottish Police Authority have been involved in a difficult and challenging investigation. 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 investigation will continue, I hope today’s announcement brings some reassurance to everyone in the community.”