Ben was 21 months old when he vanished from the island of Kos on July 24 1991, close to an old farmhouse which was being renovated by his grandparents.
His mother Kerry Grist-Needham, has always believed he was abducted and is alive.
South Yorkshire Police went to the High Court to get a blood sample taken from Ben when he was born at Boston Hospital in Lincolnshire, for the routine Guthrie heel-prick test to screen for disorders.
They needed legal authority to obtain the sample because Ben would now be over 18 and so would normally have to grant permission for the move.
Ms Grist-Needham praised South Yorkshire Police for “pulling out all the stops” and said she hoped the development would help other families of missing people as well.
She told ITV Calendar News: “It’s been a long process, over about six or seven months, but the end result is obviously amazing.”
Ben’s family hope that once police have extracted his DNA they will be able to cross-check it against databases held in other countries.
“I think probably this is the first time any mother would wish that their child’s committed an offence in whichever country that he’s in,” Ms Grist-Needham said.
“Because obviously if he’s been in trouble with the police or involved in an accident, Ben will flag up if his DNA is held by any of these authorities.”
Ben’s disappearance sparked an international hunt, with the Greek police alone logging up to 200 possible sightings of the missing child.
In the months and years after he disappeared, the most common theory was that he had been snatched by gypsies.
It has also been suggested that Ben, who would now be 22, was taken for adoption by a non-Greek family, perhaps in Scandinavia, Australia or the United States.