The Princess, who was born on Saturday May 2 at 8.34am, weighing 8lbs 3oz, will be known as Princess Charlotte.
Kensington Palace said in a short statement: "The Duke and Duchess of Cambridge are delighted to announce that they have named their daughter Charlotte Elizabeth Diana.
"The baby will be known as Her Royal Highness Princess Charlotte of Cambridge."
The naming of the royal baby Charlotte Elizabeth Diana will be seen as a tribute to the Duke of Cambridge's father, mother and grandmother.
Charlotte is the feminine form of Charles and William and the Duchess of Cambridge are likely to have had their daughter's grandfather in mind when they chose it.
William has spoken of his deep respect for his father and the amount of time the prince commits to his charitable work. "I just really hold him in great admiration," the Duke has said.
The Prince of Wales strove to protect William and Prince Harry following the death of their mother Diana Princess of Wales and backed them as they have worked to honour her memory through their charitable connections.
They, in turn, accepted and supported him when he married Camilla Parker Bowles, now the Duchess of Cornwall.
William is protective of his father, defending him against criticism he has often faced. Naming his daughter after the prince will be seen as a clear public demonstration of his love of Charles.
Charlotte is also the middle name of Kate's sister Pippa Middleton. Nicknames for the princess could include Lottie or Charlie.
French in origin, it means "petite" and "feminine" or "free man".
According to the Office for National Statistics, Charlotte was the 21st most popular name for girls in England and Wales in 2013. It has fallen in popularity over the last decade and was in 4th place in 2000.
The Duke and Duchess of Cambridge are likely to have chosen Elizabeth in tribute to the baby's great-grandmother the Queen.
And Diana was always expected to feature somewhere in remembrance of William's late mother, who died in a car crash when William was 15.
The Duke places great importance on honouring her memory, having already used Diana's sapphire and diamond engagement ring when he proposed to Kate.
The royal couple picked the bookmakers' favourite for their son George.
This time the bookies got it wrong. Alice - which was the name of one of Queen Victoria's daughters and also of the Duke of Edinburgh's mother - was their favourite for the new princess.
Royal name history
Charlotte - chosen by the Duke and Duchess of Cambridge for their new daughter - is a traditional royal name.
Queen Charlotte, who was born in 1744, was married to George III. Charlotte was actually her second name - her first was Sophie.
A keen botanist, she founded Kew Gardens, had 15 children - 13 of whom survived - and was a patron of the arts. Some historians have argued that she was of African descent.
She had an addiction to snuff, a passion for jewellery and a fondness for dogs.
Her hair was said to have gone grey with shock as she coped with her husband's so-called madness - now known to have been a blood disorder called porphyria.
Queen Charlotte and George III also named their first daughter and fourth child Charlotte. She was born in 1766 and later became known as the Princess Royal.
Charlotte, Princess Royal, was said to have been clumsy, shy and lacking in confidence.
She led a restricted life and was kept away from suitors but eventually married a Duke of Wurttemberg in Germany.
She later became Queen of Wurttemberg after Napoleon took troops into Germany and reorganised its political structure.
George IV also named his only child Charlotte in 1796 when he was the Prince of Wales.
George III said of Princess Charlotte of Wales that there "never was so perfect a little creature" and he was said to have talked endlessly of his granddaughter. She was excitable and given to tantrums as a child.
But she died tragically in childbirth at the age of 21 in 1817, leading to a mass outpouring of grief across the nation.
The new baby was, in fact, born on Princess Charlotte of Wales's wedding day.
She married Leopold of Saxe-Coburg, later King of the Belgians, on May 2, 1816 at Carlton House, the Prince Regent's London home, and crowds of people filled the streets in celebration.
William IV's first born daughter was a Charlotte - a Princess of Clarence - but she died in infancy in 1819.
William's uncle and Diana, Princess of Wales's brother Earl Spencer named his youngest daughter Charlotte Diana in 2012.
A previous Princess of Cambridge - Princess Augusta of Cambridge, who was born in 1822, had Charlotte as one of middle names. She was Princess Augusta Caroline Charlotte Elizabeth Mary Sophia Louise of Cambridge.