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It is Phillips' first child with her rugby-player husband Mike Tindall and the Queen's fourth great grandchild.
The pair are known in Britain for their sporting success with Phillips, 32, the 15th in line to the throne, winning an equestrian silver medal at the London Olympic Games in 2012 and Tindall, 35, the former captain of the England rugby union team.
The palace said in a statement: "Mrs Michael Tindall today safely delivered a baby girl at Gloucestershire Royal Hospital. 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."
Phillips is the only daughter and second child of Princess Anne, Queen Elizabeth's only daughter. Anne married Olympic equestrian Mark Phillips in 1973 but they divorced in 1992. She is now married to retired naval officer Timothy Laurence.
Phillips and Tindall met in Australia during England's Rugby World Cup campaign in 2003 and married in 2011 in Edinburgh.
Just six weeks after their marriage, CCTV footage showed Tindall hugging and kissing another woman at a bar in New Zealand, where his team was competing at the World Cup. He later apologised and said the woman was "just an old friend".