The 12 paintings were commissioned to ensure an artistic record remained of those who fought in the WW2 campaign.
Prince Charles said they captured the "spirit, resolve, warmth and humanity" of the men, shown wearing their medals.
The exhibition called The Last Of The Tide begins 71 years to the day since the Allied invasion of Europe in 1944.
Prince Charles decided to commission the portraits after attending the 70th anniversary D-Day commemorations in Normandy last summer.
He said: "It seemed to me a tragedy that there were no portraits of D-Day veterans, hence this collection of remarkable old soldiers from the regiments of which my wife and I are colonel or colonel-in-chief."
One of the veterans featured in the exhibition, Brian Stewart, who was a captain with the 1st Battalion, Tyneside Scottish said he was "immensely proud" to have been chosen.
"I remember the bravery and tenacity with which my anti-tank platoon used their six-pounder guns in Normandy at the battle of Rauray, when we destroyed at least 12 German tanks during a day-long battle," he said.
"It has been an honour to be involved in this project and to know that veterans from so many different regiments will have their portraits joining the Royal Collection."
Artist Jonathan Yeo painted the portrait of veteran Geoffrey Pattinson, who during D-Day was a sergeant with 9th Battalion, The Parachute Regiment.
"Painting someone who candidly describes the first time they set foot on foreign soil as the time they jumped out of a moving aircraft and parachuted down through flying bullets, to land in Normandy for D-Day, makes Geoffrey one of the more extraordinary sitters I've encountered in my time as a portrait artist," Mr Yeo said.
