The baby, Athena Elizabeth Rose Mapelli Mozzi, was born several weeks prematurely at London's Chelsea and Westminster Hospital on January 22.
She weighed 1.95kg.
"She is tiny and absolutely perfect," Mapelli Mozzi said in a post on his personal Instagram page.
View this post on Instagram A post shared by Edo Mapelli Mozzi (@edomapellimozzi)
"We are all (including Wolfie and Sienna) already completely besotted with her."
The princess and her husband released a photograph of their daughter, showing Athena with dark hair, wearing a white long-sleeved garment and wrapped in a pink blanket with her face hidden by her arm.
Beatrice, 36, married property developer Mapelli Mozzi in July 2020.
The couple already have one daughter, Sienna, who was born in September 2021.
Mapelli Mozzi also has a son called Wolfie, eight, from a previous relationship.
Beatrice is the ninth-in-line to the throne and the eldest daughter of Prince Andrew and Sarah, Duchess of York.
"Their majesties the King and Queen and other members of the royal family have all been informed and are delighted with the news," the statement said.
with PA
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