The proud parents couldn't wait to announce the happy news on social media, even revealing the baby name they'd chosen for their little one.
Hilaria, 32, took to Instagram on Monday to share a sweet snap of her newborn son, telling fans they've named him Leonardo Ángel Charles Baldwin.
In the photo the now mum-of-three can be seen cradling her newborn, who looks very peaceful in a pink and blue striped hat. Hilaria, who looks incredible for someone who's just given birth, captioned the photo:
'We are so pleased to introduce you to our new baby, Leonardo Ángel Charles Baldwin. It was such a special day bringing him into this world 💙'
Fans were quick to pass on their congratulations, with one commenting 'LOVE! ❤️💙❤️ Beautiful Name! Beautiful Mum -> inside and out! 😍 You and your family are gorgeous!' and another adding: 'Congratulations! Love to your beautiful family!'
Alec was seen with the couple's son Rafael just hours before his baby was born
Dad Alec, 58, took to Twitter with a simple announcement for his second son, listing the date and time of his arrival. Adding in a link to his wife's Instagram pic, he wrote: 'Leonardo Angel Charles September 12 6:51pm New York City'
Leonardo Angel Charles— ABFoundation (@ABFalecbaldwin) September 13, 2016
New York Cityhttps://t.co/aV2Ip6H8rm
Alec, who is famous for his role in 30 Rock, also shares two other children with wife Hilaria - their three-year-old daughter Carmen and one-year-old son Rafael. The couple announced baby number three was on the way in March, just nine months after welcoming their son.
Hilaria with her daughter Carmen
Alec also has a daughter, 20-year-old Ireland, whom he shares with ex-wife Kim Basinger.
In September last year, the star revealed he was excited to expand his family with his other half.
Hilaria, a yoga instructor, has stayed active throughout her pregnancy
'I'm dying to have another child with my wife,' he told People. 'I love my wife more than anything. I love our family, I'm very happy. I've never been happier before in my life,' he gushed.