Media and supporters of the royal family are waiting outside the Lindo Wing of St Mary's Hospital, Paddington, where the Duchess of Cambridge was taken after going into labour this morning.
It is reported that although she was around a week overdue, the Duchess went into labour naturally at around 6am.
Prince William is by her side in the same private wing where he and brother Prince Harry were born.
A spokesman for the couple, both 31, said: "Things are progressing as normal."
The child, whose sex is not known, will be third in line to the throne. Prince Harry moves to fourth in line.
Some devoted fans of the royal family have been camped outside the hospital for two weeks in anticipation of the birth of the future King or Queen.
The Queen is staying at Windsor Castle today and being kept informed about the progress of the labour.