Charlie Girling, of the 1st Aylesford Scouts, in Kent, collapsed on Sunday at Roihu 2016, near HÃ¤meenlinna.
The UK Scout Association said the on-site medical team and local paramedics "rendered immediate support but unfortunately were unable to save him".
Spokesman Simon Carter said it was in touch with the families of the children at the jamboree, which more than 16,000 people are attending.
"We will be working with the Finnish Scout movement and the relevant local authorities to establish the full details of this tragic incident," he added.
More than 2,800 scouts from more than 40 countries are attending the jamboree in the south of Finland.
Memorial services have been held at the event in tribute to Charlie.
Anna Munsterhjelm, chief scout in Finland, said: "The Guides and Scouts of Finland and Finnjamboree Roihu express their deepest condolences to the friends and family of the tragic medical situation that resulted in the death of a scout.
"The loss has moved thousands of people within and outside the camp.
"The camp has professional crisis counsellors that are making their utmost best that everybody has the support they require." (sic)
Charlie had been a Year 7 pupil at Maplesden Noakes School, in Maidstone.
Head teacher Jane Prideaux said staff were "deeply shocked and saddened" by his death.
"He'd been with us for just a year," she said.
"He was a lively lad, well-liked by his peers and teachers," she said.
Ms Prideaux added Charlie had been a "very hard working, very able student, with a great sense of humour".
"He was full of life, and wanted to get involved in things."
A 12-year-old scout has died at an international jamboree in Finland.