The body was found on Wednesday morning and police confirmed it was the missing schoolboy.
Kent Police Chief Inspector Mark Weller said: "It brings an end to our search and I would like to echo Lucas' family's message of thanks to those who came out to help search for him in the last few days.
"The community support we have witnessed has been heart-warming, even in the most tragic of circumstances.
"I'd also like to recognise the efforts of our partners from Kent Search and Rescue, Kent Fire and Rescue Service, HM Coastguard, the Royal National Lifeboat Institution and all the volunteers who assisted in the search for Lucas.
"While the search may have ended, our support to Lucas' family continues."
Lucas fell into the water on Saturday while fishing with his dad.
His father and two adults jumped into the water in an attempt to rescue him but he was swept away by a strong current.
Experts from the emergency services used specialist equipment in order to find Lucas - including sonar detectors, underwater cameras, divers, dogs and drones.
Hundreds of members of the public also joined in the search for the missing schoolboy.