The Queen's granddaughter gave birth to her first child, weighing 6lb 2oz, at the Chelsea and Westminster Hospital.
Buckingham Palace said the princess and her daughter were "doing well" and the baby's grandparents and great-grandparents were "delighted".
The baby girl will be 11th in line to the throne and is the Queen's 12th great-grandchild.
In a post on Twitter, the princess said she was "so delighted to share the news of the safe arrival of our daughter", thanking the midwife team and everyone at the hospital "for their wonderful care".
Beatrice is the elder daughter of the Duke and Duchess of York. She married property tycoon Mr Mapelli Mozzi in a private ceremony in July 2020.
She is stepmother to Mr Mapelli Mozzi's son Christopher Woolf, known as Wolfie, from his previous relationship with ex-fiancee Dara Huang.
A statement from Buckingham Palace said: "The new baby's grandparents and great-grandparents have all been informed and are delighted with the news. The family would like to thank all the staff at the hospital for their wonderful care.
"Her Royal Highness and her child are both doing well, and the couple are looking forward to introducing their daughter to her big brother, Christopher Woolf."
Beatrice became an aunt for the first time in February, when her sister Princess Eugenie gave birth to a baby boy named August.
Following the arrival of the Duke and Duchess of Sussex's second child - Lilibet "Lili" Diana Mountbatten-Windsor - in June, the princess herself moved from 9th to 10th in line to the throne.
The princess, who is not a full-time working royal, is vice-president of partnerships and strategy at Afiniti, an artificial intelligence software firm.
She is also patron of a number of charities, including the Forget Me Not Children's Hospice, the Teenage Cancer Trust and the Helen Arkell Dyslexia Centre.
Her husband, known as Edo, is the son of former Olympic skier Count Alessandro Mapelli Mozzi and Nikki Williams-Ellis.
Princess Beatrice was last seen in public on September 16, at the Forget Me Not Children's Hospice garden party to celebrate the tenth anniversary of Russell House.