The group, including some former commandos, placed red life jackets over their suits and medals before climbing aboard.
They were taken on a trip around Poole Harbour, where the Royal British Legion's cruise ship MV Boudicca docked on Tuesday morning.
Schoolchildren and wellwishers waved flags to greet the veterans, aged 91 to 101, as they walked down the gang plank.
Jack Mortimer, 95, spoke to the primary school pupils about his war experiences before they taught him the Baby Shark dance.
He said he was a despatch driver taking a jeep of ammunition and mortars on D-Day.
"After that I can't tell you what happened, I get so emotional about it," he said.
Mr Mortimer, from Leeds, served with 12th Ordnance Beach Detachment on D-Day.
Asked about speaking to the schoolchildren at Poole Harbour, he replied: "I can't get the words out. It's been brilliant, delightful, absolutely tremendous."
Coxswains of 1 Assault Group's 539 Assault Squadron and troops from Charlie Company of Taunton-based 40 Commando spoke to veterans both on and off the ship.
They took the heroes on three of their high-speed Offshore Raiding Craft, used in seaborne assaults, around the harbour.
Len Perry, 95, who was on destroyer HMS Beagle during D-Day, was allowed to briefly pilot one of the boats.
"This is great," he said.
"I didn't ever think I'd get the chance to do something like this again."
Poole was a significant embarkation point on D-Day, making it a fitting place for veterans to meet the green berets.
Many landing craft, gun boats and the decking for Mulberry Harbours were built in the Dorset town.
Thousands of American troops bound for Omaha beach left from Poole.
Brigadier Graeme "Jock" Fraser said it was a "great privilege" to meet the veterans.
"These D-Day veterans are at the very centre of a series of events, which will mark a pivotal phase of World War Two, when 75 years ago they took part in Operation Neptune, the largest amphibious operation in history," he said.
After the Royal Marines had left the ship, those on board watched a performance by Lance Corporal Richard Jones, 28, a magician who won Britain's Got Talent in 2016.
L/Cpl Jones, who serves with the Household Cavalry, first performed card tricks for small groups of veterans sat on the ship before a larger show in the evening.
"It is incredible to hear the experiences that they went through," he said.
"You think of the awful things they have experienced but talking to them, they are happy, having a great time, getting on well and having a laugh together.
"It is very inspirational to see."
He described the Armed Forces as "a very close knit family".
"It must be nice for these guys to chat to serving personnel because a lot has changed since they served," he said.
"A lot has also stayed the same despite the age and generational differences - everyone is on the same wavelength and gets the humour."
George Winter, from Reading, was a quartermaster with the Royal Navy on D-Day, serving on HMS Harrier.
He described the welcome at Poole as "absolutely wonderful".
"We were mine-sweeping the beaches clear of sea mines," Mr Winter said. "We led the way across the ocean so the men could get ashore without getting blown up.
"We were there on June 5, with the boys landing on June 6. As dawn came, we had to get out of the way so they could get to shore."
Mr Winter, who has five great-grandchildren, said he was "18 years, one month and three days old on D-Day".
The veterans will attend the national commemorative event in Portsmouth on Wednesday before travelling to Normandy for events in Bayeux and Arromanches.
The ship returns to Portsmouth on Saturday before concluding its journey in Dover on Sunday.