Leslie Binns, 42, from Rotherham, South Yorkshire, turned around to save Sunita Hazra, an Indian woman, who was scaling the summit ahead of him.
He said he felt "immensely proud" to have saved a life but wished he could have also helped save another climber, who died on the descent.
Mr Binns was blinded in his left eye after an explosion in Afghanistan.
He was in the Army for 13 years, serving in Bosnia, Iraq and Afghanistan and was blown up four times. He has been awarded two medals, including the Queen's Commendation for Bravery for finding improvised explosive devices in Afghanistan in 2009.
Ms Hazra, who is 32 and lives near Kolkata in India, left hospital on Wednesday.
Her brother Kingshuk Chatterjee told the BBC the family "cannot express our gratitude" to Mr Binns for saving her.
"He's the reason why she is still alive now," he said. "He is a very brave man."
Mr Binns, who now works in private security in oil fields in Iraq, said the incident happened when he was on a climb in the early hours of 21 May.
He was approaching an area nicknamed "The Balcony" - where climbing teams store spare oxygen bottles - when he noticed a "commotion" ahead of him.
"I noticed someone sliding down the fixed climbing lines towards me.
"All I could hear were the screams of terror as the person gained momentum. I braced myself to try and stop whoever it was, and managed to do so.
"At this time I didn't know that this was Sunita Hazra. I helped her upright and looked at her oxygen regulator. It was registering empty."
Mr Binns helped Ms Hazra recover and she attempted to continue her descent by herself, but collapsed after about 20 metres.
"It was at this point I decided to cancel my summit bid to help Sunita," Mr Binns said. He was about another 12 hours away from making the final ascent to the top.
"I climbed down to her and called my Sherpa. I told him we are not going up and we would give Sunita my spare oxygen bottle and take her down."
He says the descent was a perilous and difficult one, and on the way the three climbers found another man who was also struggling to descend, bringing him along with them.
Mr Binns said Ms Hazra and the other climber "kept collapsing", adding: "I fell into waist-deep crevasses no less than five times, which was very tiring, and we were also crossing blue ice which was very dangerous as we kept slipping."
Eventually he and Ms Hazra managed to reach his camp, but due to exhaustion and difficult weather conditions they were unable to bring the other climber along.
"I gave Sunita my sleeping bag in my tent. We then tried our best to get her warm by patting and rubbing her. She was suffering from hypothermia and her right hand was badly frost-bitten.
"I then remembered we had a flask of ginger tea. I used this to try and re-warm Sunita's hand. I dried it off and told her to keep it in her fleece pocket which would keep it warm."
Mr Binns says that while in his tent he heard the other climber's voice in the distance "but I was too exhausted to go back out - I literally collapsed and fell asleep".
In the morning, Mr Binns learned the other climber had been found and taken to his team. Ms Hazra's Sherpa came to collect her and help her to continue down the mountain.
But when Mr Binns continued with his own descent that next day, he came across the body of the other climber, who had died during his journey downwards.
Mr Binns believes Sherpas took the body down from the mountain, and is unsure as to how the climber eventually died.
Mr Binns said: "I truly regret not being able to do anything more for him. But I had nothing left in me that night and I tried my level best to rescue him, but he could not be moved. No summit is worth a life.
"I am immensely proud that I helped Sunita. I just wish I could have done more."
Mr Binns, who has climbed "all the major peaks in the UK", is now in Kathmandu and due to return to the UK to see his fiancee and daughter on 6 June.
"I wish Sunita and her family all the best and hope she makes a full recovery," he said.
BBC iWonder: The ups and downs of climbing Everest
A British ex-serviceman abandoned his Mount Everest climb some 500m from the summit to save a fellow mountaineer.