A statement from Buckingham Palace announced the new arrival on Friday morning.
"Mrs Michael Tindall today safely delivered a baby girl at Gloucestershire Royal Hospital," read the statement. "Mr Tindall was present at the birth. The weight of the baby was 7lbs 12oz (3.5 kg.)"
"The Queen, The Duke of Edinburgh, The Princess Royal, Captain Mark Phillips and Mike's parents, Mr Phillip and Mrs Linda Tindall, have been informed and are delighted with the news. The baby's name will be confirmed in due course."