The Oscar-winning Juno screenwriter gave birth to baby boy Marcello Daniel Maurio earlier this week.
"We had our boy early this morning! Marcello Daniel Maurio, 7lbs, 2 oz, lightly mustachioed (sic)," Cody tweeted on Tuesday.
Cody did not release any further details about the birth.
The United States of Tara producer and Maurio got married last summer and announced Cody's pregnancy in April.