The Duke and Duchess of Cambridge have left St Mary's Hospital, taking their baby daughter home tonight to start their new life as a family of four.

Prince George had already left the hospital and returned to Kensington Palace after being introduced to his sister at the Lindo Wing, where Kate gave birth just after 8.30am this morning.

William and Kate expressed their gratitude to the hospital for their support during the birth of the baby princess, who weighed 8lbs 3oz.

A Kensington Palace spokesman said: "Their Royal Highnesses would like to thank all staff at the hospital for the care and treatment they have all received. They would also like to thank everyone for their warm wishes."

George waved to crowds as he was brought to St Mary's Hospital in Paddington, London, to meet his younger sister for the first time.

William made a brief round trip to his home Kensington Palace to pick up his son for the visit.

The Duchess gave birth to the new princess just over nine hours ago. Last time she stayed overnight, but this time, after a much shorter labour, she is leaving the same day.

The baby, whose name has yet to be announced, is fourth in line to the throne, the Queen's fifth great-grandchild and a spare to the heir.

It was the first time George, who was dressed in a blue ensemble of shorts, jumper and pulled up socks, has been officially seen in public in the UK since he left the same hospital himself as a newborn just under two years ago.

The moment mirrored William's meeting with Prince Harry when his father the Prince of Wales brought him to see his baby brother in 1984.

William also affectionately kissed George's head as he carried him up the steps ahead of introducing him to his younger sister.

When George was first lifted out of the Range Rover which was driven by his father, William put him on the pavement and took his hand.

But the 21-month-old turned to the Duke and held up his arms, indicating he wanted to be picked up after seeming a little unnerved following shouts and screams from the crowds.

Proud father William spoke of his joy following the birth telling the press he was "very happy'' when he left to pick up George from Kensington Palace.

The Prince of Wales - who said he wanted his second grandchild to be a girl - and Duchess of Cornwall were left "absolutely delighted'' by the news, Clarence House has said.

William's uncle Earl Spencer also reacted with joy to the announcement, saying: ''It's wonderful news - we are all thrilled for all four of them.''

The Queen, who spent part of her day attending a military event at Richmond Castle, in north Yorkshire, was dressed appropriately in pink on the day her fifth great-grandchild was born.

A girl has not been born this high up the line of succession for 65 years since Princess Anne arrived third in line in 1950.

The baby is also the first Princess of Cambridge to be born for 182 years. The last was King George III's granddaughter, Princess Mary Adelaide of Cambridge, who was born in Hanover, Germany, in 1833.

A baby daughter was the firm favourite in the gender betting odds, with punters heavily backing the arrival of a girl.

The birth was proclaimed on Twitter, by the age-old tradition of a bulletin erected outside Buckingham Palace and by a town crier who entertained the crowds who had gathered outside St Mary's Hospital.

Palace footman George Oates, 26, from North Yorkshire, and Simon Garnett, 30, from Cumbria were given the job of placing the proclamation on an ornate gold easel in the forecourt of the Queen's official London home.

Very quickly a long queue formed as people waited patiently to get a glimpse of the brief bulletin - on foolscap-sized paper set in a dark wooden frame - which said the Duchess was "delivered" of a daughter and gave the time of birth.

It was signed by a senior medical team led by consultant obstetrician Guy Thorpe-Beeston, surgeon-gynaecologist to the household, who delivered the royal baby.

Alan Farthing, the Queen's surgeon gynaecologist, who was engaged to popular BBC presenter Jill Dando when she was shot and killed in April 1999, was also part of the team.