A spokesperson for the palace said the Queen and the Royal family were "very pleased" to hear the news.
If the baby is born after William and Kate's baby in April, it will be Queen Elizabeth's seventh great-grandchild.
Zara and Mike Tindall have announced they are expecting a new addition to their family.
A few weeks earlier the couple, who were both professional athletes, announced she was expecting.
They family made the journey after spending Christmas in Sydney during their working holiday Down Under.
Speaking about the heartbreaking miscarriage, Mike previously told The Sunday Times: "One thing you do learn is how many other people have to go through the same thing".
"We were very lucky to have Mia in terms of what we've been through", he said.
Their whole world "turned upside down" after that tragedy, Mike Tindall told The Telegraph a year ago. The couple has one daughter, 3-year-old Mia.
He continued: 'The saving grace for us has been Mia, ' adding: 'However down we feel, she will come running up in our faces'.
Her husband, 39, later said that the loss of the baby had turned their world upside down.
The couple tied the knot in July 2011 in Edinburgh during a 45-minute ceremony at Canongate Kirk followed by a lavish reception at Holyrood House.
Zara is the daughter of Anne, Princess Royal and her first husband Captain Mark Phillips.