Corporal Robert Callaghan, 40, originally from Chester, England, and his wife Hannalore, said they were “deeply upset” by the loss of their five-year-old daughter Isobel in the freak accident at an army show in Germany.
A statement issued by the British army on behalf of the couple said: “Isobel Callaghan was involved in a tragic accident whilst attending the JHQ (joint headquarters) show on Sunday.
“The Callaghan family were enjoying the show and the sunny weather minutes before Isobel was taken from them during a freak storm. Mr and Mrs Callaghan and Isobel’s little brother Stuart are deeply upset by the incident. The family have asked that their privacy is respected until they have had time to come to terms with their grief.
“Mr and Mrs Callaghan would like to pass on their heartfelt thanks to all those people who have sent messages of condolence, including the many flowers, cards and teddy bears.
“The support and prayers have been of great comfort to them. Their little angel is now sleeping, waiting until they meet again.”
The tragedy struck just after midday when the youngster became entangled in the mooring ropes of an escaped helium balloon at the show, at Rheindalen, near Monchengladbach.
A cable holding the 12ft balloon had broken free and wrapped itself around her arm during a freak storm.
Spectators watched in horror as the youngster was swept up into the air and out of sight.
Within minutes a desperate search was launched, but two hours later her body was found in the small town of Hamminkeln about 40 miles away.
Witnesses at the Rheindalen base described scenes of “havoc” and “chaos” as strong winds and heavy rain battered the showground, injuring six other spectators.
One person needed hospital treatment.
The rest of the two-day show was cancelled as a mark of respect.
Cpl Callaghan, 40, who is with the 35 Engineer Regiment, which is serving at Sennelager in western Germany, Mrs Callaghan, who is German-born, and their son Stuart, four, were being comforted by friends and bereavement counsellors.
A post mortem was due to be conducted by a pathologist who is expected to fly to Germany from Britain tomorrow.
The results are not expected until Saturday.