Though the new parents have yet to divulge their newborn's chosen name, a source told People that "Olivier hasn't left Halle's side."
"Nahla visited her baby brother earlier today," the source said of Berry's 5-year-old daughter with ex-boyfriend Gabriel Aubry.
Berry and Martinez married in France over the summer, after announcing last April that the 47-year-old actress was pregnant with her second child.
"I feel fantastic. This has been the biggest surprise of my life to tell you the truth," Berry told CNN at the time. "I 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."