The Ministry of Defence has named the soldier killed in an incident on Salisbury Plain Training Area on 15 October.
An Army spokesperson said: "It is with sadness that we can confirm the death of Private Jethro Watson-Pickering in an incident on Salisbury Plain Training Area.
"The thoughts and sympathies of the Army are with the family and friends of Pte Watson-Pickering at this very sad time.
"Wiltshire Police are investigating and therefore it would be inappropriate to comment further."
Wiltshire Police say the 23-year-old died at midday while on exercise.
The force is investigating the death, the cause of which is yet to be determined by a coroner, alongside the Army and the Health and Safety Executive.
In a statement released on Saturday, Wiltshire Police said the deceased had been "part of a crew operating an armoured vehicle" on Salisbury Plain – one of the UK's largest military training areas.
According to a statement of Facebook by The Yorkshire Regiment, Pte Watson-Pickering of the 1st Yorks Regiment was from the village of Boosbeck, in Redcar and Cleveland, North Yorkshire.
The post added: "The thoughts and prayers of the regimental family are with his family. 'Fortune Favours the Brave'."