UK police working on the missing case of the 21-month-old believe he died on the Greek island, where he vanished near his grandparents home in 1991.
British detectives flew to the island to excavate key sites after receiving information a digger driver, now deceased, may have run over the toddler.
The three-week dig culminated in the partial demolition of a farmhouse on the site where Ben, from Sheffield, was last seen on July 24 more than two decades ago.
It is thought he died on the day he disappeared.
Officers claim to have found an item of significance, which they would not elaborate on, which was with the youngster when he disappeared.
It was shown to Ben’s family.
Detective Inspector Jon Cousins said: “It is my professional belief that Ben Needham died as a result of an accident near to the farmhouse … where he was last seen playing.
Delivering a briefing summing up the 21-day dig, Det Insp Cousins said: “The events leading up to, and following up to that incident have been explored by my team and experts to great lengths.
“The fact that we have not had a direct result on this visit to Kos does not preclude the facts that we know to be true.
“During the last three weeks a number of items have been recovered from both sites.
“An item found… is of greater significance to this investigation.
“This item, which I have shown personally to Ben’s family over this weekend, was found in one of the targeted areas at the second site, very close to a dated item from 1991.
“It is our initial understanding that this item was in Ben’s possession at or around the time he went missing.
“The recovery of this item and its location further adds to my belief that material was removed from the farmhouse, on or shortly after the day Ben disappeared.”
His mother, Kerry Girst, has tirelessly campaigned for information over her son’s whereabouts in the years since his disappearance.
Speaking before the briefing, the toddler”s mother said she wanted to “tear up” the whole Greek island.
She said: “They know he”s dead but just can”t find him. Police said it”s time we ended our 25-year search.
“They are right but I can”t say goodbye knowing he”s still on that island somewhere.
“I feel physically sick. I can”t feel any worse than I do.
“Someone knows where he is. For God”s sake, help me find him. We know he”s dead but we need to find him.
“When someone dies you find a special place.”
But Mr Cousins denied the probe was ending.
He said: “We remain committed to the investigation and it will not simply close; myself and Detective Superintendent Matt Fenwick will retain ownership of it and if new information comes to light, we will investigate it thoroughly.”
Local digger driver, Konstantinos Barkas, was excavating land near the spot Ben was last seen.
Mr Barkas died of cancer last year, prompting a witness to come forward with fresh evidence, claiming he had run over the toddler, killing him by mistake.
British officers alongside volunteers from Greece excavated more than 800 tonnes of soil from two key sites, one the farmhouse where Ben was playing in front of, and a landfill a quarter of a mile away.
Some 93 items of interest have been found, with some sent back to the UK for further forensic analysis.
South Yorkshire Police said on Sunday: “The physical search of two sites on Kos, Greece, has formally come to an end.
“Work continues behind the scenes as officers begin to process the findings from each site.”