Kensington Palace officials said the infant weighed 8 pounds, 6 ounces.
The new baby -- the first for William and Kate, will be third in line to the British throne.
The royal couple's child will officially be known as His Royal Highness Prince [the baby's name] of Cambridge.
The title follows the dukedom bestowed on William by his grandmother, Queen Elizabeth II, on his wedding day in 2011. Earlier this year, the queen issued a royal decree allowing this royal baby -- and all of William and Kate's children -- to be titled prince or princess. The decree said "that all the children of the eldest son of the Prince of Wales should have and enjoy the style, title and attribute of royal highness with the titular dignity of Prince or Princess prefixed to their Christian names or with such other titles of honour."
The child’s name could take much longer to be unveiled.