Former rugby player Mike Tindall was by his 37-year-old wife’s side as she gave birth to the royal baby at Stroud Maternity Unit in Gloucestershire on Monday.
Zara, who is the daughter of Princess Anne, already has four-year-old Mia with Mike.
The new baby is 19th in line to the British throne and will be the Queen and Prince Phillip’s seventh great-grandchild.
Buckingham Palace said in a statement: “Mrs Michael Tindall was safely delivered of a baby girl on 18th June, at Stroud Maternity Unit. Mr Tindall was present at the birth.
“The Queen, The Duke of Edinburgh, The Princess Royal, Captain Mark Phillips and Mike’s parents, Mr Philip 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 second child for Zara and Mike, the fourth grandchild for The Princess Royal and the seventh great-grandchild for The Queen and The Duke of Edinburgh.”
Has Zara and Mike Tindall’s baby already broken a royal record?
The baby weighed 9 lbs 3 oz when she was born.
This has made her the heaviest royal baby in more than 100 years.
The record was previously held by Savannah Phillips, the daughter of Zara’s brother Peter Phillips.
She weighed 8lbs 8oz when she was born in 2010.
Prince Louis was not far off as he weighed 8 lbs 6 oz when he was born on April 23 this year.
Zara and Mike’s first daughter Mia weighed 7 lbs 12 oz when she was born in 2014.
The new arrival will not have a title as she is not an HRH.
Mike Tindall also doesn’t have a title and Zara, who was born down the female line as the offspring of the daughter of a sovereign, is not entitled to be an HRH.
Zara’s father, Captain Mark Phillips, is thought to have been offered an earldom by the Queen when he married Princess Anne, but he chose not to take it.
Their announcement comes more than a year after Zara suffered a miscarriage just before Christmas in 2016.