The Queen's granddaughter Zara Tindall has given birth to a baby girl weighing 7lbs 12oz (3.5kg).
Mrs Tindall's husband, rugby player Mike Tindall, was present at the birth of their first child at Gloucestershire Royal Hospital.
The Queen, the Duke of Edinburgh and the families of both parents were all delighted at the news, Buckingham Palace said.
The baby, as yet unnamed, becomes 16th in line for the throne.
Mrs Tindall later left the hospital and returned home.
Her husband expressed his joy on Twitter: "Thanks so much for all your kind messages. Definitely the best day of my life today, so happy! The girls are both doing great!"
In another tweet, he praised hospital staff, writing: "Big thanks to all involved at Gloucester Royal, they were fantastic!"
Mr and Mrs Tindall were married at Canongate Kirk in Edinburgh in July 2011.
The new arrival is the third grandchild of the Princess Royal and her first husband, Mark Phillips - and the Queen and Prince Philip's fourth great-grandchild.
The birth follows that of Prince George in July last year to the Duke and Duchess of Cambridge.
In a statement, the Queen's press secretary said: "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."
Prime Minister David Cameron said: "It's wonderful news and I'm absolutely delighted for the couple. I know them a little and I know they'll be absolutely devoted and delighted parents, so happy news all round."
BBC Royal correspondent Peter Hunt said the couple had chosen an NHS hospital, the Gloucestershire Royal, for the birth.
Mrs Tindall, 32, does not hold a royal title and is not referred to as Her Royal Highness. Her daughter will be known as Miss Tindall.
The new parents met during England's Rugby World Cup-winning campaign in Australia in 2003.
Mr Tindall, 34, a former England rugby star, is now a player-coach at Gloucester.
His wife has achieved sporting success in her own right - where she still competes under the name Zara Phillips - winning individual gold in three-day eventing at the World Equestrian Games in Germany in 2006.
The title helped her become BBC Sports Personality of the Year later that year, following in the footsteps of her mother, Princess Anne, who won the award in 1971.
As a member of the Great Britain eventing team she won a silver medal at the London 2012 Olympics.
She is planning to take part in the next Olympic Games, which will be held in Rio in 2016.