Brazilian model Rose Costa gave birth to the X-Men star's baby in Los Angeles on Friday (14Dec12).
According to People.com, the tot, a boy named William Luca, will take both his parents' last names.
Marsden already has two children with his estranged wife Lisa Linde, who filed for divorce from the actor in September, 2011 - son Jack Holden, 11, and daughter Mary James, seven.
The 39 year old dated Costa briefly after the end of his marriage.
A representative for the hunk has yet to comment on the report.