Hilaria, 29, was admitted to New York's Mount Sinai Hospital on Friday after going into labor. "We are overjoyed to announce the birth of our daughter Carmen Gabriela," the new mom tweeted late Friday. "She is absolutely perfect."
This is the first child for the couple, who married in June 2012. Baldwin also has a 17-year-old daughter, Ireland, with his ex-wife Kim Basinger.
Baldwin can currently be seen on the big screen in Blue Jasmine.