According to sources, the couple is blessed with a boy, reports usmagazine.com.
Information on the baby's name and other details have not been revealed yet.
The couple, who got married in April, announced the pregnancy in June.
Dornan will next be seen in the upcoming movie "Fifty Shades Of Grey", where he will be seen essaying the lead role of Christian Grey. He replaced actor Charlie Hunnam to take on the role.