The actor's fiancee Dominique Geisendorff gave birth to son Rekker on 23 January (13), and Gigandet has shared the happy news with fans on his Facebook.com page.
The newborn is a younger sibling for the couple's three-year-old daughter Everleigh.
Gigandet declares, "Dominique gave birth to our second child, son Rekker Radley Gigandet, on 1/23/2013. He is healthy, happy, and perfect.
"We are humbled to have the opportunity to call ourselves the parents of this beautiful soul, and I am forever grateful to God for allowing me to know this kind of boundless, immaculate love. Thanks to those of you who wish to send your positive energy and well wishes."
The couple has been engaged since 2008.
Gigandet played evil vampire James in the first Twilight film.