In identical statements posted to their Instagram accounts, Diaz and Madden said their newborn "instantly captured our hearts and completed our family."
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Citing a "strong instinct to protect our little one's privacy," the couple said they "won't be posting pictures or sharing any more details other than the fact that she is really really cute." Diaz and Madden did not specify exactly when Raddix was born.
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They continued: "From our family to all of yours, we're sending our love and best wishes for a Happy New Year and Happy New Decade."
Diaz, 47, and Madden, 40, have been married since 2015. Diaz is known for her roles in "There's Something About Mary" and "Being John Malkovich" as well as the "Charlie's Angels" and "Shrek" franchises.
Madden is best known as a member of the band Good Charlotte and his later performances with his twin brother, Joel Madden, as The Madden Brothers.