Actress Halle was said to have given birth to their son on Saturday 5 October after being admitted to Cedars Sinai Hospital in Los Angeles.
According to TMZ, thrilled parents Halle and Olivier have now decided upon the Spanish name Maceo Robert - which means 'gift of God'.
Although Olivier is French, his father Robert was a Spanish professional boxer who was born in an area of Morocco, which was previously a Spanish zone.
Their baby boy is the couple's first child together and a little brother for Halle's daughter from a previous relationship, Nahla.
Prior to his birth, Halle - who married Olivier in France in July - was spotted out and about with a huge baby bump.
See who else has given birth this year in our gallery below:
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