updated 01/17/2014 AT 8:00 AM ET
•originally published 01/17/2014 AT 9:00 AM ET
Zara, 32, welcomed a daughter Friday, Buckingham Palace announced. The Olympic equestrian and her husband, rugby player Mike Tindall, have not confirmed a name for their child yet.
The baby girl, who weighed 7 lbs., 12oz., becomes 16th in line to the throne, after her mother, who is 15th.
Mike Tindall was at Gloucestershire Royal Hospital for the birth, the palace said. He tweeted his thanks to the hospital staff.
“Thanks so much for all your kind messages. Definitely the best day of my life today, so happy.! The girls are both doing great!” he wrote.
The baby is Zara’s first, and becomes the third grandchild for Zara’s mother, Princess Anne. (Zara’s brother, Peter Phillips, has two young children.) Along with George, Queen Elizabeth now has four great-grandchildren.
The palace said in a statement: “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.”
Everything appears to have gone so well for mom and baby that Zara was able to leave the publicly funded hospital in Gloucester within a few hours of giving birth, PEOPLE has learned. She is believed to have headed to her home on her mother’s Gatcombe Park estate.
Zara – commonly known as Zara Phillips – grew up near William at Gatcombe Park, and the cousins are close, something that was further confirmed when she was chosen as one of Prince George’s godparents by William and wife Kate.