Private Cameron Laing died after being struck by a trailer at Bracken Tor youth hostel near Okehampton, west Devon, on Tuesday evening.
The 20-year-old, who served with 7 Theatre Logistic Regiment Royal Logistic Corps, suffered a cardiac arrest after a head injury.
Pte Laing, from Nottingham, and his partner were expecting a baby boy, and had already named him Cameron.
In a statement released by police, his family and partner said: "Cameron was an amazing son, brother, boyfriend and expectant father.
"He was a loveable rogue, always playing practical jokes and the fun in any situation.
"He couldn't wait to be a father to his son.
"He will be sorely missed by everyone whose life he touched."
Devon and Cornwall Police said an investigation into the incident was continuing.
Pte Laing was struck by an uncoupled trailer and pinned against the towing vehicle.
"Both the towing vehicle and trailer were military items and were part of a small convoy heading towards Okehampton battle camp," a force spokesman has said.