The next thing the world wants to know is what the royal baby will be named, and what Prince William and Kate will be like as parents. HELLO! Online has chatted to well-wishers outside Buckingham Palace and the Lindo Wing to hear their thoughts and predictions.
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What do you think the royal baby will be called?
"I think George is a nice name, or Harry," said Rachel Evans from Cambridge, who was accompanied by her friend Rachel Ash. The duo had travelled especially to London this morning to wait outside the Lindo Wing in the hope of meeting Kate and giving her a heartfelt gift.
"We wanted to give this lovely doll to Kate," said Rachel. "It's a limited edition Baby born doll holding a polo mallet. Prince William is into his polo so we thought it was quite fitting."
While George has been tipped as a likely possibility, with odds running at 3/1, it is unlikely Harry will be chosen as the royal baby's first name as Prince William's own younger brother, Prince Harry, already takes the name.
That hasn't stopped royal watchers from hoping and betting on the name James though, which is the name of Kate's sibling, and currently stands at 4/1.
Newlyweds Craig and Gemma Owen, who were passing through London before they set off for their honeymoon, pushed for the traditional name.
"Personally I'd like James," said Craig. "It's a long time since we've had a James. We've had Georges in the last 200 years, so I'd like James. I think keep it traditional. I heard Alexander being pushed around, but I'm not so sure."
Before the royal baby's birth, the majority of the betting population speculated Prince William and Kate's firstborn would be a princess called Alexandra. The male counterpart, Alexander, has also emerged as a possible choice, with odds running at 7/1.
"I think Francis would be fitting because of the connection to Diana and Kate's father," said Nicole Russell, who is on holiday from Canada.
Francis has also been hot on the bookies' lips, making reference to the middle names of both Kate's father's, Michael Middleton, and Prince William's mother, Princess Diana, who took the female equivalent.
How do you think Princess Diana would have felt about the baby's birth?
All of those chatting to HELLO! Online said Princess Diana would have undoubtedly been proud and happy for her son and daughter-in-law on their special day.
"Princess Diana would have loved Kate and she'll be looking down on her and Prince William," said Claire.
"I think she would have been proud," agreed Rachel, while Chris from California said Princess Diana would "be so happy".
"She would have been amazing," said Savanna from the US, accompanied by her media student friends. "She would have been so proud and an incredible grandmother."
What do you think the royal baby's birth will mean for Britain?
Prince William and Kate's firstborn has now replaced Prince Harry as third-in-line to the throne, and those interviewed by HELLO! Online believed Baby Cambridge's birth was a positive thing for the nation. Apart from uniting the population with joyous news, it was another momentous occasion that the UK could be proud of, following the Queen's Diamond Jubilee celebrations and the Olympics last year.
"I think it's good because the baby will be a new young icon for people to look up to," said Rachel. "Our generation has Prince William and Harry to relate to."
"This time last year it was the Olympics and now the baby," said Ruth from Ireland. "There's a lot happening for Britain."
"The birth is great for the country," said Nicole. "Look at all the tourists — it's great for the mood, the atmosphere, the country."
"I think the royal family are wonderful," said Nicole from Manchester. "Even before Kate and William and Harry — they just do so much for the country. The Queen is absolutely beautiful — I love her."
What kind of parents do you think Prince William and Kate will be?
While it is speculated that Prince William and Kate will be "devoted" and "hands-on" parents, the question of whether their children's lives will be quite as "normal" as they hope for has been debated.
"I think they'll be great parents," said Craig. "When everyone says 'they're going to make it as ordinary as possible' though, I grin because there's no way it could be ordinary."
"They'll be hands-on parents — I think the days of royals passing their parenting role over to nannies is gone," he added, with Nicole agreeing, saying, "They will be really involved and loving, and continue on as Princess Diana did."
"I'm hoping that Kate's going to be quite close to the baby and not have a nanny," said Joanna from London, carrying her baby son who was donning a crown. "I breastfeed and think Kate should too."
Claire, meanwhile, imagined the first-time parents to do their utmost in providing their children with a normal upbringing. "Prince William and Kate will be very devoted and keep it as normal as possible," she said. "They'll carry out their duties, but also protect their children."
"They look like a really happy couple," said Savanna. "They're model citizens."
What do you think Prince Harry will be like as an uncle?
Prince Harry's reputation as a fun, young royal will make him the perfect uncle to William and Kate's firstborn, and the public interviewed are already imagining Prince Harry taking his nieces and nephews on nights out, but also giving a lot of support to the first-time parents.
"I think he'll be really good," said Rachel. "He's been pictured changing a Baby born doll's nappy before, hence why we brought the doll today."
Nicole agreed, saying, "He'll be really involved. He'll be doing some pub crawls with his nephews and nieces."
"He'll have that wild side to him," said Ruth. "I think he's been quite supportive of Kate too."
"He'll be giving all the things he shouldn't give the baby," said Nicole from Manchester. "He'll feed him ice cream, chocolate, and drive around fast in his car."
Savanna, meanwhile, thought the newborn would have an effect on Harry's attitude. "It will change him," she said. "He won't be 'wild Harry' in the tabloids anymore."