Zara Phillips and Mike Tindall have named their daughter Mia Grace Tindall.
Tindall made the announcement via the social networking site, saying, "For everyone who has asked what our daughters name, it's Mia Grace Tindall."
Zara gave birth earlier this month at Gloucestershire Royal Hospital to her first child, which weighed 7lbs 12oz.
The baby is the Queen's fourth great grandchild.
Tindall took to Twitter after the birth to describe his joy at becoming a father for the first time, saying it was "definitely the best day of my life".