Noah Shannon, their first child, was born Sept. 27, UsMagazine.com said.
"We have been very lucky to have had a peaceful few weeks at home," the actress wrote on Facebook Wednesday.
"He is healthy, happy, and perfect," she said.
"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. May God bless you and your families abundantly."
Green also has a 10-year-old son from a previous relationship with actress Vanessa Marcil.