Writer and fitness instructor Hilaria, 36, shared a photo of herself holding the newborn boy with her 778,000 Instagram followers.
She wrote: “We had a baby last night. He is perfect and we couldn’t be happier. Stay tuned for a name.”
The news comes after the couple revealed in November last year that Hilaria had suffered a miscarriage.
In a social media post, Hilaria said she and the actor were “devastated” at being told their unborn baby had died at four months.
They had already lost another child in April.
Baldwin, 62, is best known for TV series 30 Rock, films including The Aviator and The Departed, and for his impersonations of US President Donald Trump on Saturday Night Live.
He also has a 24-year-old daughter, called Ireland, from his previous marriage to Kim Basinger.
Hilaria married Baldwin in 2012.
