Keeping the sex of the baby a surprise until the delivery day, the Palace revealed that Kate had given birth to a healthy baby boy, with both mom and baby doing well.
William and Kate have not yet disclosed the name of the infant prince. Arthur is one of Prince William's second names, along with Philip and Louis, while Prince Harry's full name is Henry Charles Albert David.
The little boy's parents William and Kate are one of the most famous and influential couples in the world, but would have seemed like any other doting mother and father to the newborn, who arrived safely on Monday morning United Kingdom time.
And when another member of the crowd suggested the name Alexander, he joked: "Funny you should say that".
Still another woman quipped: "Kate Middleton leaving the hospital after giving birth looks better than I'll look on my wedding day".
William and Kate waited two days before announcing both George and Charlotte's names.
Reports seem to be focusing on the fact that Prince William might have "nodded off" during his first public duty since the birth of his new baby.
In its statement, the palace said that Catherine had been taken by vehicle from Kensington Palace to St. Mary's Hospital in Paddington, in the northwest part of the city. She also looked sensational.
He has also become fifth in line to the throne, relegating Prince Harry to sixth in line.
"It is tradition that a framed notice of birth goes on display on a ceremonial easel on the forecourt at the Palace", the statement continued.
The Duke of Cambridge may have given a hint to naming his newborn son when he described a Kiwi guest as having a "strong name".