24 July 2013 Last updated at 02:23 ET
The proud parents are still working on a name
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Prince Charles will attend the Royal Welsh Show in Powys with the Duchess of Cornwall, a day after meeting his grandson for the first time.
The prince said he is "thrilled and very excited" after his grandson was born on Monday, and he and Camilla visited the baby on Tuesday afternoon.
The royal couple are honouring an engagement made earlier this month to appear at the Llanelwedd show.
It will be the prince's seventh visit to the show, the duchess's first.
Charles is a former president of the Royal Welsh Agricultural Society (RWAS) which runs the event, and his mother The Queen is patron.
After news broke that the Duke and Duchess of Cambridge had a baby son on Monday, the RWAS said it was "delighted with the news of a new royal baby".
New grandfather Prince Charles met the new arrival on Tuesday evening
The society passed on its "best wishes and congratulations on this momentous occasion" and said it shared "a real sense of pride in welcoming a patron of the future".
The RWAS has promised a "packed itinerary" for the royal couple and for guests hoping to catch a glimpse of them.
Charles and Camilla will begin their visit in the President's Pavilion meeting RWAS staff.
The prince will then attend the cattle ring, main ring and sheep ring, and a reception for the Prince's Countryside Fund, of which he is president.
The fund gives grants to projects supporting people who look after the countryside.
The Duchess of Cornwall will visit the food hall and Green Pavilion, where she will meet some of the RWAS's Young Members Forum.
As president of the Royal Voluntary Service (RVS), she will also visit the RVS hut.
The charity supports older people through community services like meals on wheels.
The royal couple were greeted by cheering crowds of well-wishers on a visit to East Yorkshire on Tuesday, just a day after after the birth.
Many people congratulated them on the birth of the baby boy.
The duchess told the BBC: "It's wonderful for the grandfather - he's brilliant with children."
On Tuesday evening, Prince William and his wife emerged from St Mary's Hospital in London and showed the baby to waiting media.
William said: "He's got a good pair of lungs on him, that's for sure. He's a big boy, he's quite heavy.
"We are still working on a name so we will have that as soon as we can."
Prince Charles first visited the Royal Welsh Show in 1969 and again in 1988, 1995, 1999, 2000 and 2001, when he opened the society's Winter Fair.
The show's royal connections go back to 1907 when, three years after the society was founded, the then Prince of Wales - the future King George V - became patron.
The royal family have regularly supported the show throughout the society's history.
In 1966, three years after it settled on a permanent site in Llanelwedd, the late Princess Margaret became the first royal visitor to the new showground.
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Prince Charles will attend the Royal Welsh Show in Powys with the Duchess of Cornwall, a day after meeting his grandson for the first time.
The prince said he is "thrilled and very excited" after his grandson was born on Monday, and he and Camilla visited the baby on Tuesday afternoon.
The royal couple are honouring an engagement made earlier this month to appear at the Llanelwedd show.
It will be the prince's seventh visit to the show, the duchess's first.
Charles is a former president of the Royal Welsh Agricultural Society (RWAS) which runs the event, and his mother The Queen is patron.
After news broke that the Duke and Duchess of Cambridge had a baby son on Monday, the RWAS said it was "delighted with the news of a new royal baby".
The society passed on its "best wishes and congratulations on this momentous occasion" and said it shared "a real sense of pride in welcoming a patron of the future".
The RWAS has promised a "packed itinerary" for the royal couple and for guests hoping to catch a glimpse of them.
Charles and Camilla will begin their visit in the President's Pavilion meeting RWAS staff.
The prince will then attend the cattle ring, main ring and sheep ring, and a reception for the Prince's Countryside Fund, of which he is president.
The fund gives grants to projects supporting people who look after the countryside.
The Duchess of Cornwall will visit the food hall and Green Pavilion, where she will meet some of the RWAS's Young Members Forum.
As president of the Royal Voluntary Service (RVS), she will also visit the RVS hut.
The charity supports older people through community services like meals on wheels.
The royal couple were greeted by cheering crowds of well-wishers on a visit to East Yorkshire on Tuesday, just a day after after the birth.
Many people congratulated them on the birth of the baby boy.
The duchess told the BBC: "It's wonderful for the grandfather - he's brilliant with children."
On Tuesday evening, Prince William and his wife emerged from St Mary's Hospital in London and showed the baby to waiting media.
William said: "He's got a good pair of lungs on him, that's for sure. He's a big boy, he's quite heavy.
"We are still working on a name so we will have that as soon as we can."
Prince Charles first visited the Royal Welsh Show in 1969 and again in 1988, 1995, 1999, 2000 and 2001, when he opened the society's Winter Fair.
The show's royal connections go back to 1907 when, three years after the society was founded, the then Prince of Wales - the future King George V - became patron.
The royal family have regularly supported the show throughout the society's history.
In 1966, three years after it settled on a permanent site in Llanelwedd, the late Princess Margaret became the first royal visitor to the new showground.