Duke and Duchess of Cambridge, William and Kate with their baby daughter

The Duchess of Cambridge has given birth to a baby girl.

Kensington Palace have announced that both mother and child are doing well.

She was born just after half past eight this morning.

The baby girl is fourth in line to the throne.

An unofficial town crier took centre stage and confirmed the royal birth.

Unofficial town crier gives news of the birth. Image: Screen grab from BBC News.

Shortly before 4 pm Prince William, the Duke of Cambridge left the hospital to cheers and drove to Kensington Palace.

He waved to the crowd and said his wife and daughter were very happy.

Prince William leaving St Mary’s Hospital Paddington after the birth of his baby girl earlier. Image: Screen grab from Sky News live feed.

Prince William went back to the Palace to pick up their first born, Prince George, to take him to St Mary’s to show him his new sister.

Prince William taking his son, 21 month old Prince George, to see his newly born sister. Image: Screen grab from live Sky News Feed.

Shortly after 6 pm, William and Kate appeared with their baby daughter to show the waiting media and crowd.

There were loud cheers at Kate, pointed to the baby girl born just after 8.30 in the morning.

They went back inside the hospital to pick up a baby carrier that the Duke of Cambridge used to convey his baby daughter into his car.

They drove off in a convoy of cars to return home to Kensington Palace.

Her Royal Highness The Duchess of Cambridge was safely delivered of a daughter at 8.34am.

— Kensington Palace (@KensingtonRoyal) May 2, 2015

The baby weighs 8lbs 3oz. The Duke of Cambridge was present for the birth.

— Kensington Palace (@KensingtonRoyal) May 2, 2015

The Queen, The Duke of Edinburgh, The Prince of Wales & The Duchess of Cornwall, Prince Harry & members of both families have been informed

— Kensington Palace (@KensingtonRoyal) May 2, 2015

Her Royal Highness and her child are both doing well.

— Kensington Palace (@KensingtonRoyal) May 2, 2015

HMS Lancaster, known as the ‘Queen’s Frigate’, sent a message of congratulations to @KensingtonRoyal on the new birth pic.twitter.com/gBPY85Atp0

— Royal Navy (@RoyalNavy) May 2, 2015

The easel at Buckingham Palace giving details of the birth of The Duke and Duchess of Cambridge’s daughter today pic.twitter.com/0yp1lNi462

— BritishMonarchy (@BritishMonarchy) May 2, 2015

The Duke of Cambridge leaving the hospital to see Prince Grorge https://t.co/e2FCimAxEm

— Kensington Palace (@KensingtonRoyal) May 2, 2015

Sky News have set up a live digital video feed from the entrance to the Lindo wing that is being transmitted on YouTube.

[Live video of the Lindo Wing front door at St Mary’s Hospital, London, as the world waits to see the Duke and Duchess of Cambridge with their baby daughter born earlier today. The camera will move off the door when other patients are entering or exiting the hospital.]

The news that Kate went into labour this morning was broken to the public on Kensington Palace’s Twitter feed.

HRH The Duchess of Cambridge was admitted at 06.00hrs to St Mary’s Hospital, Paddington, London and is in the early stages of labour.

— Kensington Palace (@KensingtonRoyal) May 2, 2015

The Duchess travelled by car from Kensington Palace to the Lindo Wing at St. Mary’s Hospital with The Duke of Cambridge.

— Kensington Palace (@KensingtonRoyal) May 2, 2015

It’s a girl! If you are welcoming a new addition to your family, post a photo using #WelcomeToTheFamily for our blog pic.twitter.com/7v56mTmxpH

— Kensington Palace (@KensingtonRoyal) May 2, 2015

The outgoing Prime Minister and Deputy Prime Minister and other political leaders sent their best wishes to the Royal Couple.

David Cameron

Congratulations to the Duke and Duchess of Cambridge on the birth of their baby girl. I’m absolutely delighted for them.

— David Cameron (@David_Cameron) May 2, 2015

Nick Clegg

Congratulations to the Duke & Duchess of Cambridge on the birth of their new baby. Miriam & I wish them all the best as their family grows

— Nick Clegg (@nick_clegg) May 2, 2015

Ed Miliband

Congratulations to the Duke and Duchess on the birth of their daughter. Wishing them lots of joy and happiness – and hopefully some sleep!

— Ed Miliband (@Ed_Miliband) May 2, 2015

Nigel Farage

Congratulations to the Duke and Duchess of Cambridge on their new baby girl. 8lbs, 3oz. It’s great to see a return to imperial measures!

— Nigel Farage (@Nigel_Farage) May 2, 2015