The French president and first lady welcomed a baby girl on Wednesday in Paris, marking the first time a ruling French president has become a father while in office since Napoleon.
In a post on her official website, Bruni thanked those who had sent well-wishes and congratulations upon hearing the news of the birth and revealed the child's name for the first time.
"I am deeply touched by the many messages of congratulations that I have received since the birth of our daughter Giulia," she wrote.
"On this happy occasion, my husband joins me in expressing our warmest thanks to all those of you who sent us these tokens of your kindness."
Bruni, who confirmed her pregnancy in July, has vowed to protect her child from the media and promised not to release photos to the press.