The Queen is "delighted" with the birth of her first great-grandchild, Buckingham Palace has said.
The baby girl, the first child for the Queen's eldest grandson Peter Phillips and his wife, Autumn, weighed 8lbs 8oz.
The newborn, who is 12th in line to the throne, was born in Gloucestershire Royal Hospital on Wednesday. Her name has not yet been confirmed.
Mr Phillips, son of Princess Anne, met his wife in Montreal in 2003, and they wed at Windsor Castle five years later.
A statement from Buckingham Palace read: "The Queen, the Duke of Edinburgh, the Princess Royal, Captain Mark Phillips and Autumn's family have been informed and are delighted with the news."
Canadian-born Mrs Phillips, a former Roman Catholic, was accepted into the Church of England shortly before their wedding in May 2008.
Her husband would have had to give up his right to the throne had she not done so.
Since 1701, heirs to the throne marrying Catholics cannot become sovereigns.
Peter Phillips is the only son of Princess Anne and her first husband, Captain Mark Phillips. He does not have a royal title because his mother turned down the Queen's offer of honours for both her children.
Peter's younger sister Zara Phillips announced her engagement to the rugby player Mike Tindall earlier this month.