Lance Corporal Joe Spencer, of 3rd Battalion The Rifles, died at RAF Tain in the Scottish Highlands on 1 November.
A document published on the MoD website, called “Training and exercise deaths in the UK armed forces: 1 January 2000 to 5 November 2016”, states that the 24-year-old died in a live fire accident at the “range waiting point”.
L/Cpl Spencer, from Hampshire, joined the Army in 2011 and had completed a tour of Afghanistan as part of Operation Herrick 16.
Around 30 detectives were said to be involved in the investigation into his death.
The MoD document shows there were 139 deaths during Armed Forces training between January 2000 and November this year.
The death of Private Conor McPherson at Otterburn Training Area in Northumberland is also documented as a live fire accident, which took place during Exercise Wessex Storm 4 in August.
The cause of death for Corporal Josh Hoole, of The Rifles, who died after collapsing while on pre-course training for the Platoon Sergeants’ Battle Course in Brecon, Mid Wales, is listed as “natural cause” in the publication.
It had been linked by some to training on what was the hottest day of the year on 19 July.
Tributes were paid to all three after their deaths.
L/Cpl Spencer was described as a “good soldier and a good lad”, and political leaders, including First Minister Nicola Sturgeon and Prime Minister Theresa May, sent their condolences to the soldier’s loved ones.