The 44-year-old took to Twitter to share the happy news, tweeting: "Christian and I are delighted to announce our baby boy was born this morning weighing 7lbs 8oz."
This marks the first child that the couple have had together.
Geri is also mum to 10-year-old daughter Bluebell from a previous relationship, Christian Horner – the boss of Red Bull's Formula One team – shares one-year-old Olivia with ex Beverley Allen.
Although the Horners have yet to reveal their little lad's name, it is believed that the honour of choosing it will fall to big sister Bluebell.
A source told Bang! Showbiz: "Geri wants to include Bluebell in the pregnancy as much as possible to ensure she doesn't feel left out – especially after being an only child for so long.
"She's taken Bluebell along to scans and has given her the role of helping her and Christian choose a name for her new sibling, as well as picking out accessories for the nursery.
"Bluebell is really excited about having a sister or brother to play with."
Emma Bunton, Geri's former Spice Girls bandmate, whose birthday also happens to be today, was quick to tweet her congratulations, writing: "Amazing news, so happy! #birthdaytwins #birthdaymade love you all. Xxx."
Meanwhile, Pregnant TV presenter Alex Jones chimed in: "@GeriHalliwell congratulations!!! Lovely news. Don't think I'll be far behind you."
Fans also flooded the social media site to share their well wishes.
"Congratulations Geri & Christian!" another added.
With a third chipping in: "Congratulations Geri! Hope you and the Spice boy are doing well."