The 31-year-old hunk wed English musician Warner in April this year and they announced the pregnancy news in June.
Warner, who performs under the name Slow Moving Millie, recently gave birth to a baby boy and Dornan is "thrilled" to become a father, reported Us magazine.
The actor's representative has declined to comment on the news.
The baby's arrival comes at a busy time for Dornan. He was cast as the leading man in the upcoming 'Fifty Shades of Grey' film adaptation in October and will spend the Christmas holidays on location in Vancouver, Canada, where the raunchy movie is set.