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Britain's Prince William and Catherine Duchess of Cambridge greet people after launching the King's Cup Regatta in London, Britain May 7, 2019. Ben Stansall/Pool via Reuters Image Credit: REUTERS

They have grown up as brothers-in-arms, teasing one another fondly but mercilessly through every stage of their lives so far.

So when the Duke of Sussex became a father for the first time on Monday, it was only right that his older brother was on hand to celebrate in his own inimitable style, telling him: “Welcome to the sleep deprivation society that is parenting.”

The Duke of Cambridge spoke for the Royal family when he said he was “absolutely thrilled” about the newborn baby boy’s safe arrival, saying they could not wait to welcome him in person soon.

The Duchess, already a mother of three children, spoke of the “really exciting time” for the new Sussex parents and, perhaps mindful of the pressure she felt in her early days with Prince George, empathised that the first few weeks were “always a bit daunting”.

The Prince of Wales, in Berlin for his first day of a short overseas tour to Germany, made an affectionate reference to the baby in a speech.

Last night, he told guests at a garden party it was a “particular pleasure” to return to the city as the grandfather of a newborn grandson.

Speaking earlier in the day, he had said: “We couldn’t be more delighted at the news, and we’re looking forward to meeting the baby when we return.”

Baby Sussex is believed to have spent his first two days in the world tucked up quietly at Frogmore Cottage with his proud parents.

Today, he will be introduced to the world in a photocall in Windsor, after his father promised the new family would step out “to share it with you guys and so everyone can see the baby”.

The newborn’s name and title are also expected to be announced this week, along with introductions to senior members of the Royal family.

The Queen is currently at Windsor Castle, but was yesterday on duty at an Order of Merit lunch with the Duke of Edinburgh. Both were “delighted” with news of their eighth great-grandchild, a spokesman has said, with the Queen happily accepting congratulations during the semi-public engagement.

Doria Ragland, the Duchess’s mother, is known to be staying at Frogmore Cottage, on hand to help care for and dote on her first grandchild.

Outside of cottage walls, it was business as usual for the Royal family, with members stopping to answer questions about the baby and share their joy.

“Obviously thrilled, absolutely thrilled, and obviously looking forward to seeing them in the next few days when things have quietened down,” the Duke of Cambridge said.

“I’m very pleased and glad to welcome my own brother into the sleep deprivation society that is parenting.”

The Duke of Sussex has already shown some of the effects of his new phase in life, admitting he had only managed a few hours of sleep before announcing the birth on Monday and appearing so dazed in front of the television camera that he thanked a pair of horses for good behaviour.

Asked whether he had any pearls of wisdom for his younger brother, as a father of three, the Duke of Cambridge laughed and said: “Plenty of advice, plenty of advice... But no, I wish him all the best and I hope the next few days they can settle down and enjoy having a newborn in their family and the joys that come with that.”

The Duchess, who was alongside her husband at the Cutty Sark in Greenwich, south-east London, to launch a charity King’s Cup Regatta event, said: “We’re looking forward to meeting him and finding out what his name’s going to be, so it’s really exciting for both of them. These next few weeks are always a bit daunting the first time round so we wish them all the best.”

Reflecting on the Cambridge and Sussex cousins, she added: “It’s such a special time, obviously with Louis and Charlotte just having had their birthdays, it’s such a great time of year to have a baby. Spring is in the air.”

In Germany, the Prince of Wales and Duchess of Cornwall also found the public a little preoccupied with baby fever. During a walkabout, Frank-Walter Steinmeier gave the Prince a teddy bear to take home, telling him: “Let me congratulate you.”

The Prince said: “Thank you, I’m collecting a rather large number of them.”