David Capstick was walking in the mid Wales national park Saturday when he met the soldiers in a distressed state.
Relatives of L/Cpl Craig Roberts, 24, from Penrhyn Bay, Conwy, paid tribute saying he had died “in the pursuit of his dream”.
Defence Secretary Philip Hammond announced a full inquiry.
Speaking to Channel 4 news, Mr Capstick described how he was walking in the Beacons when he was passed by a line of soldiers moving in the opposite direction at five or 10-minute intervals.
“We then came across two soldiers who had clearly broken that intended mode of operation and were proceeding slowly together, and one of the soldiers made a compassionate plea for some drinking water for his colleague,” he said.
“He was upset,” he added. “The other soldier was trying to make the best of the situation and asked if we could spare any water for his colleague, not for himself.”
Mr Capstick added that it “certainly was slightly odd” that the two soldiers in particular had bunched together and were “clearly in distress.”
In a statement issued through the Ministry of Defence, Mr Roberts's father Kelvin said: “We are all devastated at the loss of our beloved Craig; this has left a massive hole in all our lives.”
He said he had died “in the pursuit of his dream”.
Mr Roberts, who had worked as a teaching assistant in London, was due to take up a job in Whitehall in the office of Education Secretary Michael Gove.
He had served with the Territorial Army (TA) for more than five years and was a member of the 3rd Battalion Royal Anglian Regiment.
It is believed he served as a reservist in Iraq and Afghanistan, and had taken part in several exercises including a training mission in Texas with the American National Guard.
He had taken part in a four-week trial for the TA SAS reservists ending in a 40-mile (64km) hike over the Brecon Beacons.
L/Cpl Roberts was described as being “the salt of the earth” by one friend, who added that the soldier was “extremely dedicated”.
The University of Leicester economics graduate was described by Professor Ali al-Nowaihi as a “very promising young man – independent, strong willed and determined”.
BBC security correspondent Frank Gardner said he understood the deaths occurred after the SAS training and preparation phase, right at the start of the selection phase.
He also understood there were extra water supplies available in the area, in addition to the water the men were carrying.
SAS selection course
The Brecon Beacons is home to the Infantry Battle School and makes up one of Britain's largest military training areas.
According to the MoD website, the SAS (Reserve) selection course is run twice a year and consists of two main components – “aptitude” and “continuation”.
The “progressively arduous” aptitude phase is designed to select volunteers with the right qualities, including physical and mental robustness; self-confidence; self-discipline; the ability to work alone; and the ability to assimilate information and new skills.
The continuation training – after passing aptitude – is an intensive period of instruction and assessment on Special Forces tactics, techniques and procedures, including weapons and standard operating procedures.