The baby is also a second cousin to Prince George, Princess Charlotte and Prince Louis.
The couple have not yet revealed their daughter's name but another announcement will be made "in due course" according to the official statement.
The new baby is believed to be the heaviest royal baby in recent years, taking over the record from Zara's niece Savannah Phillips, who was 8lb 8oz when born in 2010.
The palace says the queen and other senior royals are "delighted with the news".
'Mrs Michael Tindall was safely delivered of a baby girl on 18th June, at Stroud Maternity Unit.
Zara Tindall gave birth to her second child with husband Mike today, with Buckingham Palace confirming the happy news that they had welcomed a baby girl.
The new royal, who is now 19th in line to the throne, arrives two months after the birth of Elizabeth's sixth great-grandchild, Prince Louis, the third child of her grandson Prince William and his wife Kate.
Mrs Tindall, who is the daughter of the Queen's only daughter, the Princess Royal, married Mr Tindall in 2011.
Zara and former rugby player Mike are already parents to daughter Mia, four.
This baby is the seventh great-grandchild for The Queen and The Duke of Edinburgh.
The little girl weighed 4.16kg (9lbs 3oz).
Mike has since opened up about their loss, praising their daughter Mia for being their "saving grace".
Zara's father and mother are Captain Mark Phillips and Princess Anne. "However down we feel, she will come running up in our faces".
News of the miscarriage broke on Christmas Eve 2016, just weeks after the pregnancy was announced at the end of the previous month.