Mackenzie is the 16th person in the UK known to have died after getting into trouble in open water during the recent hot weather.
Ch Supt Pete Thorp, district commander for Doncaster, thanked the local community for their support and expressed his condolences to everyone affected by the news.
“First and foremost, on behalf of all who have been involved in the operation to find Mackenzie since Saturday, I send deepest sympathies to his family and friends,” he said.
“Losing a child is every parent’s worst nightmare and I know the impact this news will have on the wider community and particularly Mackenzie’s school.”
Thorp also expressed his thanks to those involved in the search, in particular volunteers from the Woodhead Mountain Rescue.