Their daughter, Ilaria Catalina Irena Baldwin, was born on Thursday weighing 6 pounds, 13 ounces (about 3 kilograms) Hilaria confirmed on Instagram.
"We are so excited to introduce you to our tiny dream come true," the mother wrote in the caption, alongside a compilation of images and videos of the birth and of the baby's siblings meeting her for the first time.
"Both she and I are happy and healthy. Her Baldwinito siblings are spending the day bonding and welcoming her into our home."
"How grateful we feel to welcome our newest little daughter into this world," the couple told People magazine. "Just as magical and filled with love as every other little person we have been blessed with."
The couple are also parents to Carmen Gabriela, 8, Rafael Thomas, 7, Leonardo Angel Charles, 5, Romeo Alejandro David, 4, Eduardo "Edu" Pao Lucas, 23 months, and Maria Lucia Victoria, 18 months, via surrogate.
Alec also has a daughter, Ireland Baldwin, 26, with ex-wife Kim Basinger.
Hilaria announced the pregnancy in March on Instagram.
“After many ups and downs over the past few years, we have an exciting up and a huge surprise: another Baldwinito is coming this fall,” she wrote, adding a yellow heart emoji. “We were pretty sure our family was complete, and we're beyond happy with this surprise.”
The photo she shared on social media was of the moment the couple told their children. “Our new baby is a very bright spot in our lives,” she wrote.
On October 21 last year, Baldwin was involved in the fatal shooting of cinematographer Halyna Hutchins on the New Mexico set of the Western film, Rust. Her family is suing him and the movie's other producers, alleging their “callous” disregard in the face of safety complaints on the set led directly to her death.
Baldwin, who was to star in the film, was pointing a gun at Hutchins inside a small church during the set-up for a scene when it went off, killing Hutchins and wounding the director, Joel Souza.
Hilaria's post did not mention the death.
She called her pregnancy a “blessing and a gift during such uncertain times”.
Scroll through the gallery below to see photos of Alec Baldwin on the set of Rust
- Additional reporting from AP