The yoga instructor gave birth at the Mount Sinai Hospital in New York on Friday, and proudly took to Twitter to share the news.
"We are overjoyed to announce the birth of our daughter Carmen Gabriela. She is absolutely perfect. @ABFalecbaldwin @IrelandBBaldwin," wrote Hilaria.
Baby Carmen Gabriela is the first child for Alec and Hilaria. The 30 Rock actor is also father to his daughter Ireland Baldwin, with his former wife, actress Kim Basinger.
Ireland, 17, was quick to welcome the happy news, and shared her joy on Twitter.
"I was born October 23. Carmen was born Friday, August 23. ❤," posted the model. She then wrote a touching letter addressed to her newborn stepsister and published it on her Tumblr page.
"Dear Carmen," began the letter. "You have entered the world! Welcome! We have all been anticipating your arrival!
"Girl, you haven’t even met them, but there are a ton of people who care about you... There are so many things I want to tell you, though it is best that you discover those truths on your own.
"There are countless lessons that I want to teach you, but I have faith that you will learn a majority of them on your own journey and they will help you grow."
Ireland then continued by sharing some of her own "little knowledge" about the facts of life, and giving the newborn some treasured advice.
"I love you, Carmen. You have been born into one crazy family," ended the letter. "I promise you I will always be there for you no matter what! Never forget!"
Earlier this week, Hilaria opened the doors of the couple's New York apartment and gave fans a video tour of the baby's beautiful nursery.
The new mother revealed that she and Alec get emotional whenever they step inside, saying, "We have shed tears when we come in here because it makes it real."
Hilaria had previously revealed her plans for a natural birth, and the couple had also announced in March that they were expecting a baby girl.