The two other soldiers, Edward Maher, 31, and Craig Roberts, 24, died after temperatures reached 29.5 Celsius during the training exercise on July 13 in the Brecon Beacons mountain range in south Wales.
The men were members of the Territorial Army, Britain's reservist force, who were hoping to join the elite Special Air Service (SAS) regiment.
British Defence Secretary Philip Hammond has announced a full inquiry into the incident.
In a statement issued on Tuesday, the MoD said: "It is with great sadness that we can confirm that a third army reserve soldier injured during a training exercise in the Brecon Beacons has died of his injuries.
"The family have asked for a period of grace before he is named and request that this is respected by the media."
The Brecon Beacons offer some of Britain's most rugged terrain, and the mountain range is regularly used for military training exercises.
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