The 47-year-old actress confirmed the couple had welcomed a baby girl on Instagram, and also revealed they had named their daughter Raddix.
The Hollywood star and guitarist, 40, both shared a message on their respective Instagram accounts.
The couple said they were “overjoyed” to welcome Raddix but that they felt “a strong instinct” to protect her privacy and did not intend on sharing any pictures.
The message read: “Happy New Year from the Maddens! We are so happy, blessed and grateful to begin this new decade by announcing the birth of our daughter, Raddix Madden.
“She has instantly captured our hearts and completed our family.
“While we are overjoyed to share this news, we also feel a strong instinct to protect our little one’s privacy.
“So we won’t be posting pictures or sharing any more details, other than the fact that she is really really cute!! Some would even say RAD:)
“From our family to all of yours, we’re sending our love and best wishes for a Happy New Year and Happy New Decade…”
The Mask actress married the musician in 2015 in an intimate ceremony at their home in Los Angeles, after dating for eight months.
Nicole Richie, who is married to Benji’s twin brother Joel, helped introduce the pair.
Guests at the bash included Gwyneth Paltrow and Reese Witherspoon, while Drew Barrymore was a bridesmaid and Nicole’s son Sparrow a ring bearer.
Later that year Benji cemented their romance by getting her name tattooed across his chest.