Sergeant Gavin Hillier, 35, was shot on Thursday during a night-time training exercise, the Times reported.
Sergeant Hillier, from Pontypool, served in the regiment’s motor transport platoon and was due to go Iraq this summer.
He was killed at the gunnery ranges at the Castlemartin training area in the Pembrokeshire coast national park.
Sergeant Hillier, who had served in Iraq and Afghanistan, died doing “the job he loved”, his family said.
Writing on Facebook Sergeant Hillier’s father said: “Absolutely devastated to be writing this post, probably the hardest I’ve ever had to do. At 3.45 this morning I received a phone call that will forever change my life.
“My eldest son was in a fatal accident, in the army, the job he loved. Sleep tight and rest in peace son. I’m so proud of you. Goodnight and God bless. Love your heartbroken dad.”
An Army spokesperson said: “It is with great sadness we can confirm the death of a soldier on March 4.
“Our thoughts are with his family and friends at this tragic time.
“The circumstances surrounding this death are being investigated and it would be inappropriate to comment any further.”
Sergeant Hillier had been awarded a Long Service and Good Conduct medal by the Prince of Wales Colonel of the Welsh Guards, in 2019.
According to the Ministry of Defence website, the Welsh Guards have a “dual role” as a “light role infantry” as well as “world class ceremonial soldiers, guarding the Royal Family and Royal palaces such as Buckingham Palace and the Tower of London and conducting State Ceremonial duties”.
Previous incidents at the Castlemartin ranges have claimed the lives of soldiers.
In 2017, Corporals Matthew Hatfield and Darren Neilson of the Royal Tank Regiment died from injuries they suffered after their tank exploded during a training exercise on a firing range.
A 21-year-old soldier, Michael “Mike” Maguire, died at Castlemartin in 2012 after being shot in the head while relaxing at a safe location just outside the training range.
A 2013 inquest into his death heard he was hit in the temple by a single machine gun bullet fired by a fellow soldier during a training exercise.
The inquest jury ruled Ranger Maguire, who was a member of the 1st Battalion, The Royal Irish Regiment, had been unlawfully killed.