Carole and Michael Middleton, the parents of The Duchess of Cambridge Kate Middleton, paid a visit to the newly-born royal baby on Tuesday, and the first-time grandparents could not hide their excitement.

The proud grandparents were seen arriving on Tuesday afternoon (London Time) at the Lindo Wing of St. Mary's Hospital. After an hour, Carole and Michael took time to share their experience to the press before leaving the hospital.

 "He's absolutely beautiful. We are so thrilled. They are both doing really well," said Carole, when asked about her feeling during her first encounter with their royal grandchild as reported by Telegraph UK.

When asked about how she felt during her first cuddle with her grandson, Carole said: "Amazing, It's all coming back."

Carole also added that Kate and Prince William are having a fabulous time with their baby boy at the hospital, while also denying rumors that she was asked to suggest a name for the baby boy.

Initial reports also suggested that Carole and Kate's sister Pippa were present at the birth of the royal baby, but the grandparents' "first" visit on Tuesday confirmed that those were just plain rumors.

Prince Charles and Duchess Camilla also issued a statement shortly after the baby boy was born on Monday, expressing excitement regarding the firstborn son of Prince William and Duchess Catherine.

"Both my wife and I are overjoyed at the arrival of my first grandchild. It is an incredibly special moment for William and Catherine and we are so thrilled for them on the birth of their baby boy," Charles said in a statement.

Prince William and Duchess Kate have spent their first night with their baby boy at home after leaving the hospital on Tuesday evening. When asked about the name of their firstborn son, Prince William said that they have yet to decide, but added that they are already "working on a name" and will choose as soon as possible.

The royal baby, who will be the third in line to the throne, is expected to be given a name with the style HRH Prince (name) of Cambridge. Previous rumors suggested that the royal couple decided to name their child "George".

Prince William did not deny nor confirm the rumor when asked by BBC's royal correspondent Peter Hunt.