Hilaria announced the baby news on Friday via Twitter.
"We are overjoyed to announce the birth of our daughter Carmen Gabriela. She is absolutely perfect," the new mom gushed.
Carmen is the couple's first child and is little sister to Baldwin's 17-year-old daughter, Ireland, whom he shares with ex-wife Kim Basinger.
The teenager penned an open letter to little Carmen upon her arrival, bestowing some sisterly advice about growing up the child of a celebrity.
"You have been born into one crazy family," Ireland wrote.
"We are going to have so much fun together I promise you I will always be there for you no matter what!"
Hilaria and Alec married in June 2012 after a year of dating.
- Cover Media