RGM released a statement saying Marais gave birth to Scout Edie Stewart on Wednesday.
"It is with much joy and pride that Jessica Marais and James Stewart announce the birth of their baby girl, Scout Edie Stewart,"the statement read.
"Scout was born on Wednesday 9th May at 5:41pm. Baby, Mum and Dad are doing well."
Media reports say Scout was born at Sydney's Royal Prince Alfred Hospital.
The couple met on the set of Network Seven's Australian family drama Packed to the Rafters, when they played opposite each other as on-screen lovers.
Marais and Stewart were engaged last October and not long after announced they were expecting their first child.
Marais left Packed to the Rafters early in 2011 to pursue a career in Hollywood and only recently made her international debut in the US drama Magic City.
Stewart announced this week he was leaving the Seven soapie to relocate to the US to be a stay-at-home-dad, in support of his wife's major career break.
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