The men – who have been named only as 1A and 1B – were accused of failing to take reasonable care for the health and safety of reservists participating in a 16-mile march in the Welsh national park in July 2013.
Lance Corporals Craig Roberts and Edward Maher were pronounced dead on the mountain range after suffering heatstroke during the exercise.
More than two weeks later Corporal James Dunsby died at Queen Elizabeth Hospital, Birmingham, of multiple organ failure.
The judge ruled that 1A and 1B, who were safety officers for the march, had no case to answer.
Prosecutors alleged they had committed fundamental and basic mistakes on a personal error that that led to the deaths, while a number of enquires identified systemic failures.
Judge Jeff Blackett found they had a lack of training on risk assessment and heat illness, and that other officers in their position would not have acted differently.
“I have determined that there is no evidence of negligent performance of duty when the conduct of these defendants is measured against the reasonable serviceman of similar experience, knowledge and training,” he said.
“A board properly directed could not properly convict and I intend to stop the case now.”