The Duke and Duchess of Cambridge's daughter has become fourth in line to the throne, pushing Prince Harry down to fifth.
Their new baby will not be leapfrogged by any future younger brothers after a major shake-up of the rules governing royal succession.
The changes which came into force in March, affect babies born after October 28 2011.
But the new Princess of Cambridge will not be expected to be crowned sovereign and will join second-born Royal children as being known as the "spare to heir".
The baby is the first girl born to the British royal family to take the title princess for 25 years.
She is also be the highest-ranking female in line to the throne.
It is also the first time a great granddaughter of a still-serving Monarch has been born in direct succession on the male line since 1897.
A girl has not been born this high up the line of succession for nearly 65 years. Princess Anne was born third in line in 1950 and will be 12th in line following the new arrival.
Princess Beatrice - currently the highest ranking woman in the line of succession - was born fifth in line in 1988.