Neil Heritage, from Poole, Dorset, wants to become the first above-the-knee amputee to conquer the 4,478m (14,692ft) summit in Switzerland.
The ex-corporal was blown up by a suicide bomber in Iraq in 2004 and has endured numerous operations.
Mr Heritage, 35, is due to begin his climb on 28 August using two types of specially-designed prosthetic limbs.
Since losing his legs, Mr Heritage has completed triathlons, learned to ski and rowed across the Atlantic Ocean in the Row2Recovery team.
He said: "In the first few years post injury, the idea of walking and leading a normal life seemed out of reach.
"Now being able to attempt this challenge makes me realise how far things have come.
"I hope it encourages others dealing with physical and mental injuries to follow their dreams and realise there is life beyond injury."
Mr Heritage will climb with a professional local mountain guide and former British Army soldiers Steve Green and Mark Hooks.
His attempt is being supported by the Endeavour Fund, which helps the recovery and rehabilitation of wounded, injured and sick service personnel and veterans through sport and adventure.
A double amputee army veteran who was told he would never walk again is attempting to climb the Matterhorn.