The baby weighs 9lbs 3oz and was born on Monday in Stroud Maternity Unit.
The baby is the seventh great-grandchild of Elizabeth and her husband Prince Philip. "The weight of the baby was 9lbs 3oz", the palace said.
'The baby's name will be confirmed in due course, ' Buckingham Palace said in the official statement.
The baby is 19th in line to the throne and the Queen and the Duke of Edinburgh's seventh great-grandchild.
The newest addition to the royal family is a younger sister to four-year-old Mia Tindall.
Months later, in an interview with The Times, Tindall's husband - a former England rugby captain - opened up about the family's painful loss, telling the British newspaper that their now 4-year-old daughter, Mia, was their "saving grace".
Zara is the daughter of Princess Anne and the granddaughter of the Queen.
The couple first announced they were expecting their second child in late November.
Speaking about the miscarriage previous year, Mike described his daughter Mia as a "saving grace" during the hard tie.
Like her mother, the new baby will not automatically be give a HRH title.
Ex-England rugby captain Mr Tindall, was a member of the 2003 Rugby World Cup winning team and Mrs Tindall is an equestrian champion, winning a silver medal at the London 2012 Olympics. They announced their engagement in December 2010 and married in July 2011.