The Puerto Rican star says his husband and twin sons have "fallen in love" with the new arrival.
Martin announced the baby's arrival on Instagram, showing off a picture of her tiny hands.
The Living La Vida Loca star posted: "We are beyond happy to announce that we have become parents to a beautiful and healthy baby girl, Lucia Martin-Yosef.
"It has been a special time for us and we can't wait to see where this stellar baby will take us. Both her beautiful brothers and me and Jwan have fallen in love with Lucia."
Martin already has twin sons, Matteo and Valentino, born in 2008 via a surrogate mother.
The Puerto Rico-born singer's acting role in TV series The Assassination of Gianni Versace also earned him an Emmy nomination last year.