It is a second child for the Oscar winner, who married French actor Martinez in July.
The healthy baby, who was born in Cedars Sinai Medical Center in Los Angeles, has a 5-year-old sister, Nahla, Berry's daughter with ex-boyfriend Gabriel Aubry.
A source at the hospital told PEOPLE on Saturday night, "Olivier hasn't left Halle's side. Nahla visited her baby brother earlier today." On Sunday, the big sister was seen happily skipping and prancing in the corridor of the maternity floor.
Earlier this week, only days before the birth, the 47-year-old star looked gorgeous and chic as ever, shopping at the Grove in L.A. with her daughter.
In April, Berry said about the impending arrival: "This has been the biggest surprise of my life, to tell you the truth.
"Thought I was kind of past the point where this could be a reality for me. So it's been a big surprise and the most wonderful."