The child was born at London’s Chelsea and Westminster Hospital on September 18, weighing 6 pounds and 2 ounces.
Beatrice and Mapelli Mozzi confirmed Sienna’s name on social media and shared an image of an imprint of her feet.
“We are all doing well and Wolfie is the best big brother to Sienna.”
Five-year-old Christopher Mapelli Mozzi, known as Wolfie, is Mapelli Mozzi’s son from a previous relationship.
“Feeling so much love and gratitude for my amazing wife, baby Sienna and Wolfie. These are the days I never want to forget. This week, a friend said to me the sweetest saying….that with every child you grow a whole new heart
“A massive thank you to the Midwife and the amazing team at the Chelsea and Westminster Hospital.”
He added a love heart, a kiss and a baby emoji to his message.
Sienna Elizabeth is not the only one of the Queen’s great-grandchildren to have been born this year with a name that pays tribute to the monarch.
In June, Prince Harry and Meghan, Duchess of Sussex welcomed their second child, a daughter. The couple named her Lilibet “Lili” Diana Mountbatten-Windsor, a nod to the Queen’s childhood nickname and to Harry’s mother, the late Princess Diana.
Sienna Elizabeth Mapelli Mozzi will be 11th in line to the throne, and is the Queen’s 12th great-grandchild.
In February, Beatrice’s younger sister, 31-year-old Eugenie, gave birth to a baby boy named August Philip Hawke Brooksbank.
CNN’s Max Foster and Lauren Said-Moorhouse contributed to this report.