She was born at Gloucestershire Royal Hospital, weighing 7lbs 12oz.

Phillips, a member of the eventing at the London Games, and her husband Mike Tindall, a member of the England rugby team that won the World Cup in 2003, announced the pregnancy in July.

It meant Phillips, the 2006 world champion and winner of the BBC Sports Personality of the Year award, could not take part in the 2013 European Championships in Malmö, Sweden.

Zara Phillips is presented a silver medal by her mother, Princess Anne, Princess Royal after the eventing team jumping final at London 2012 ©Getty Images

The newest royal baby, the couple's first child, is 16th in line to the throne and the fourth great-grandchild to the Queen and Duke of Edinburgh.

Buckingham Palace, who said Tindall was present at the birth, added in a statement: "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."

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July 2013: Zara Phillips to miss European Championships after announcing pregnancy