Zara and Mike Tindall have named their newborn daughter Mia Grace.
Former England rugby player Mike Tindall tweeted:
Zara Phillips gave birth at Gloucestershire Royal Hospital last Friday.
Mia Grace Tindall is the Queen's fourth great-grandchild and is 16th in line to the throne.
Zara Tindall's London 2012 team-mate - three-day eventing rider Tina Cook - has said she is very, very pleased by the news of the latest royal baby.
The Olympic medallist told ITV News she has been in touch with Zara since the birth and described her as "very excited" on the arrival of her first child:
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.
New mother Zara Tindall has returned home from the Royal Gloucestershire Hospital with her daughter.
The newborn, whose name is yet to be released, weighed 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."
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."
Zara Phillips has given birth to a baby girl at Gloucestershire Royal Hospital, her husband Mike Tindall was present at the birth. The weight of the baby was 7lbs 12oz, Buckingham Palace announced today.
Zara, whose pregnancy was announced today, is a silver medal-winning Olympian and one of Britain's leading equestrian riders.
The royal took a tumble while competing at the Barbury International Eventing and Show in Marlborough, Wiltshire, a few days ago.
But she was described as "fine" by a spokeswoman for Juniper Sport, a PR and sports agency that represents Ms Phillips.
Asked if Zara still had the next Olympics on her schedule now she was a prospective mother the spokeswoman said: "She can still compete, it totally depends on horses and whether she feels it's appropriate."