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The baby's father Mike Tindall has announced his daughter's name via Twitter as Mia Grace Tindall. Mia is 16th in line to the throne.
Zara Philips and Mike Tindall have spent their first night at home with their daughter in Gloucestershire.
There's still no news from Gatcombe Park yet on what they've decided to call the baby but Mike Tindall has been tweeting that yesterday was definitely the best day of his life and that mother and baby are doing well.
Buckingham Palace said 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."
Zara Tindall has given birth to a girl at Gloucestershire Royal Hospital. Her husband, former England rugby player, Mike Tindall was by her side.
The baby is the Queen's fourth great-grandchild, and she is sixteenth in line to the throne.
The family have already returned to their home on the Gatcombe Park Estate.
Our Gloucestershire Corresponent, Ken Goodwin, is there:
Mike Tindall has tweeted his joy following the birth of his first child with his wife Zara. The couple's daughter, whose name is yet to be released, was born this morning weighing 7lbs 12oz.
Princess Anne's daughter Zara Tindall has given birth to a girl at Gloucestershire Royal Hospital. The baby is the Queen's fourth great grandchild and weighed in at 7 pounds and 12 ounces.
Zara's husband Mike Tindall, the former England rugby star, was present at the birth.
Our Gloucestershire Correspondent Ken Goodwin was live at the hospital on our lunchtime news:
New mother Zara Tindall has returned home to Gatcombe with her daughter.
The newborn, whose name is yet to be released, was born at the Royal Gloucestershire Hospital weighing 7lbs 12oz.
Zara and Mike Tindall's baby daughter will not bear a royal title, it has been confirmed.
The former England rugby player has no title himself and Zara, born down the female line, is not entitled to be an HRH. Her father Captain Mark Phillips was believed to have been offered an earldom by the Queen when he married Princess Anne but chose not to take it.
The latest addition to the Royal Family will be known as Miss Tindall and the new parents are hoping their laid-back approach to life will rub off on their first born daughter.
Ahead of the birth, they were interviewed by Australian Women's Weekly, with Mike saying: "I think we're both quite well-balanced and laid-back as a couple, so hopefully he or she will pick up on that."
Zara added: "I hope we're going to make good parents. That's the plan."
Gloucester Rugby have tweeted their congratulations to player Mike Tindall and his wife Zara, who gave birth to a baby girl this morning:
Zara Phillips has given birth to a girl at Gloucestershire Royal Hospital.
Her husband - former England rugby player Mike Tindall - was present at the birth, a statement from Buckingham Palace has said. The weight of the baby was 7lbs 12oz.
A statement from Buckingham Palace reads: "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.
"This baby is the first child for Zara and Mike, the third grandchild for The Princess Royal and the fourth great-grandchild for The Queen and The Duke of Edinburgh, and is 16th line to the Throne."