The newborn – who is fourth in line to the throne – was “safely delivered” at 08:34 BST, the palace said in a statement.
Prince William was present for the birth of the baby, who weighs 8lbs 3oz (3.7kg).
Both Kate Middleton and her daughter are “doing well”, the statement added.
The Duchess of Cambridge had earlier been admitted to the Lindo Wing at St Mary’s Hospital where Prince George was born in July 22, 2013.
The statement from Kensington Palace added: “The Queen, the Duke of Edinburgh, the Prince of Wales, the Duchess of Cornwall, Prince Harry and members of both families have been informed and are delighted with the news.”
The royal baby girl joins the line of succession behind her grandfather Prince Charles, father Prince William and brother Prince George.
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