The happy couple have chosen to name their first child Maceo Robert Martinez, according to TMZ.
'Maceo' originally comes from Spain and was popular between the ninth and 14th centuries. It evolved into Matteo and then Matthew over time. Robert is thought to be in honour of Olivier's Spanish father.
The name Maceo is very special to the couple. "They chose it because it means gift from God," a source told E! News. "Olivier wanted to give a nod to his Spanish roots. They picked the name a while ago, they love it."
Halle, 47, and Olivier welcomed their son on Saturday 5 October at Cedars Sinai Hospital in Los Angeles.
Maceo is Halle's second child — she has a five-year-old daughter Nahla from her previous relationship with Gabriel Aubry.
The little girl is delighted to be a big sister. A source at the hospital told People that Nahla spent the weekend visiting her baby brother, and on Sunday was seen happily skipping and prancing in the corridor of the maternity unit.
She was certainly in high spirits as her step-dad Olivier treated her to a day out at the Mr Bones Pumpkin Patch on Monday.
The 47-year-old sweetly held hands with the five-year-old as they strolled through amongst the pumpkins and hay bales.
Nahla transformed into a little tigeress during the outing, getting her face painted while Olivier patiently waited, and she picked up a new festive friend — a green Frankenstein doll.