"Thanks so much for all your kind messages," tweeted Mike on Friday. "Definitely the best day of my life today, so happy! The girls are both doing great!"
"Big thanks to all involved at Gloucester Royal, they were fantastic! #newglawsfamilymember," added Mike, referring to the Gloucestershire rugby club he plays for.
Mike's close friends were quick to jokily reply to the new dad, with rugby star David Flatman saying the couple had chosen to call their daughter Dave, after him.
Mike and Zara's little girl is their first child together, Princess Anne's third granddaughter, Queen's fourth great-grandchild and 16th in line to the British throne.
The couple's daughter, who was born at an NHS hospital in near to the couple's home in Gloucestershire, is already at home with her proud parents.
A statement from Buckingham Palace announced the new arrival on Friday morning.
"Mrs Michael Tindall today safely delivered a baby girl at Gloucestershire Royal Hospital," read the statement. "Mr Tindall was present at the birth. The weight of the baby was 7lbs 12oz (3.5 kg.)"
"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."