The schoolboy, from the Eastwood District Scouts in Newton Mearns, was on holiday with a team of leaders and friends from the group when the accident happened.
He has been named locally as Elliot Alexander Peacock. It is understood his family have now travelled to Italy.
Eastwood District Scouts commissioner, Jimmy Patterson, confirmed the tragedy and said: "Measures are in hand to support the parents, young people and their leaders."
The incident happened at the Lillaz Falls, about 1800m above sea level, in the Gran Paradiso National Park on Sunday.
The Scout Association said in a statement: "We are aware that a 14-year-old Explorer Scout sadly passed away yesterday afternoon. The young person was taking part in a holiday to the Aosta Valley in Italy organised by Acorn Adventure who are a company specialising in adventure-based trips.
"We are working with Acorn Adventure to support the family, leaders and other young people involved in this very sad event.
"We are devastated that a young person has died and our thoughts and prayers are with the family and friends of the young person at this time.
"The deceased was a member of the Pegasus Explorer Scout Unit which is linked to the 35th Glasgow Scout Group."
Outdoor education provider Acorn Adventure said he was part of a group jumping into water under instruction.
"Although he was immediately rescued from the water and given CPR, tragically he could not be resuscitated," the company said in a statement.
It added: "The thoughts and condolences of all at Acorn Adventure are with his family and friends; the team's efforts are fully focused on ensuring they are supported in any way possible.
" The group were on the second full day of their nine-day adventure activity trip in northern Italy when the incident happened. They were jumping into the water, where instructors were waiting for them.
"All participants were wearing buoyancy aids, wet suits and helmets as is standard on this activity, carried out by hundreds of participants every year for the past 18 years.
"As yet it is unclear why this participant lost consciousness as he entered the water. Despite very swiftly being given CPR by trained first aiders and nurses who attended the scene, very sadly paramedics were unable to resuscitate him.
"Acorn Adventure continues to work with the Italian emergency services and the Foreign and Commonwealth Office to ensure he is brought home to his family swiftly and respectfully and senior operations staff are travelling to Italy to provide all possible support.
"Acorn would like to thank the Italian medical team for their rapid response and assistance. The Acorn team will continue to support the family in any way possible, while gathering information to establish exactly what happened."
An East Renfrewshire Council spokeswoman said: "We are devastated to learn of the death of one of our young pupils yesterday, whilst on holiday in Italy. Our priority is to provide whatever support is required to the year group and to the family, whilst we wait for news on the circumstances of this tragic incident. We are aware that the family are on their way to Italy and our thoughts are with them at this profoundly sad time."