Bruni's husband, French President Nicolas Sarkozy, visited the clinic earlier Wednesday but left after 20 minutes in order to travel to Frankfurt for eurozone debt talks, BBC states.
Reuters reports that Bruni gave birth around 8 p.m. local time. Sarkozy returned to the clinic a few hours after the birth.
Before giving birth, Bruni said the baby's photos will remain private, despite the intense public interest in her first child with Sarkozy.
Bruni gave birth at La Muette clinic in Paris. Security has been tight at the maternity clinic, which is surrounded by photographers under huge pressure to get the first shot of Baby Bruni-Sarkozy, the Guardian reports.
Crowds of well-wishers had also gathered outside the clinic, and a security cordon had to be set up, according to the BBC.
In a recent interview, Bruni said she would not share baby photos with the public.
"I will never show pictures of this child, I will never expose this child," she told TF1 program Sept a huit.
"I think exposure to public life is a choice to be made by an adult," she said, according to a translation by People magazine.
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Bruni, 43, who has kept a low public profile throughout her pregnancy, recently told French newspaper La Parisien that she was bored of being pregnant.
"Quite frankly, I can't stand it any more. I spend most of my time either sitting down or lying down. I can't drink or smoke any more. I'm in a hurry to get it over with," she said.
Bruni has a son named Aurelien from a previous relationship, while Sarkozy has three sons from earlier marriages.
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