The 30 Rock actor and his yoga instructor wife Hilaria welcomed a baby girl, Carmen Gabriela, to the world on 23 August.
Hilaria was quick to announce the arrival on Twitter, writing, "We are overjoyed to announce the birth of our daughter Carmen Gabriela. She is absolutely perfect. @ABFalecbaldwin @IrelandBBaldwin."
The newborn is the first child for Hilaria and Alec. The talented actor is already father to 17-year-old daughter Ireland who welcomed the happy news on her own Twitter account, and wrote a touching letter to her little step-sister.
"Dear Carmen," began the letter. "You have entered the world! Welcome! We have all been anticipating your arrival!
"I love you, Carmen. You have been born into one crazy family," it continued. "I promise you I will always be there for you no matter what! Never forget!"