Zara Phillips and Mike Tindall have named their baby daughter Mia Grace.
Former England international rugby star Tindall tweeted: "For everyone who has asked what our daughters name, it's Mia Grace Tindall."
Zara gave birth last week to the 7lbs 12oz girl, who is 16th in line to the throne and 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".
Zara, a silver medal-winning Olympian, who is one of Britain's leading equestrian riders, gave birth to her first child at Gloucestershire Royal Hospital with her husband at her side.
The early betting was on a more traditional name for the new royal baby with Charlotte, Victoria, Anne and Elizabeth among the front runners.
But bookmakers William Hill said Mia entered the betting yesterday afternoon at odds of 16-1 and finished as the 5-1 favourite.
William Hill spokesman Rupert Adams said: "It looks like a few people managed to get Mia correct and we have now lost for the second time running.
"We might have to close that betting early for the next royal baby - be it William or Harry."
The baby girl follows Zara's brother Peter Phillips' two children and Prince George to become the Queen and the Duke of Edinburgh's fourth great grandchild.
Peter Phillips' daughters Savannah and Isla Phillips were also born at Gloucestershire Royal Hospital in Gloucester.
Zara and Tindall moved back to Anne's Gatcombe Park estate last January after selling their regency home in Cheltenham.
The pair first met in a Sydney bar when Tindall was in Australia for the 2003 Rugby World Cup.
They married in July 2011 in a ceremony staged in Edinburgh and attended by the Queen and senior royals.
Zara won a silver medal at London 2012 with eventing equestrian teammates William Fox-Pitt, Mary King, Tina Cook and Nicola Wilson, and is planning to take part in the Rio de Janeiro Games in 2016.