"It went ideal, flawless jump", he said, according to the Associated Press. "I feel very proud that I took part in it".
Rice, who was strapped to a parachutist who controlled their flight during their tandem jump, was one of several veterans set to jump in northern France, the day before the 75th anniversary of the June 6 landings by 150,000 Allied troops.
As he landed in Sannerville, he had with him the medals of his wife Kate's great-uncle Lieutenant Richard Prince - who jumped in on D-Day as part of the 7th (Light Infantry) Parachute Battalion.
Many troops were violently seasick, some drowned, while others were gunned down as soon as landing craft opened their hatches.
"At this time of reflection for veterans of the conflict and their families, I am sure these commemorations will provide an opportunity to honor those who made extraordinary sacrifices to secure freedom in Europe", the queen said.
Reenactments over Carentan have become more common in recent years, and veterans themselves have been returning more frequently, even though a lot of them remain on the ground.
"As I host leaders from around the world today to mark this significant moment in our shared history, we will together reflect on the continued importance of the western alliance for all our countries' security and prosperity", she said.
"I represent a whole generation, the whole USA", Rice said.
The Battle of Normandy on June 6, 1944 led to the liberation of Europe and helped bring about the end of World War II the following year.
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Code-named Operation Overlord, the invasion was the largest amphibious assault in history and involved nearly 7,000 ships and landing craft.
The 1944 mission with the Army's 101st Airborne Division was "the worst jump I ever had", Rice said.
With the number of veterans of World War II dwindling, the guests of honor at an global ceremony in Portsmouth were several hundred men, now in their 90s, who served in the conflict - and the 93-year-old British monarch, also a member of what has been called the "greatest generation".
Mixing sombre recitals of soldiers' last letters home with period song-and-dance numbers, the ceremony in Portsmouth drew more than a dozen world leaders including Canada's Justin Trudeau, France's Emmanuel Macron and Germany's Angela Merkel.
D-Day veteran Les Hammond, 94, says he's thrilled to be taking part in Wednesday's remembrance events - and not bothered in the slightest that the presence of President Donald Trump and the other world leaders might be taking some of the focus away from veterans like him.
Rice is jumping in tandem with another parachutist and has been training for six months.
"We shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender", Churchill said.
The D-Day 75 National Commemorative Event will tell the story of D-Day using musical performance, testimonial readings and military displays including a fly-past of 25 modern and vintage aircraft.